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REVIEW 2 major objections 6 minor 95 references

Analytic Standard Errors for Latent Gaussian Discrete-Valued Multivariate Time Series

T0 review · 2 major / 6 minor · reviewed 2026-07-12 · grok-4.5

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Pith's one-line read Analytic standard errors for Yule–Walker estimates of latent Gaussian VAR dynamics on discrete multivariate series make Wald-type inference feasible.

desk verdict Clean, usable asymptotic SEs for an already-proposed latent-Gaussian discrete VAR; the math and sims hold up under the regimes they target. read the letter →

arxiv 2607.02732 v1 pith:56XIRARX submitted 2026-07-02 stat.ME

Christopher M. Crawford , Marie-Christine Düker , Younghoon Kim , Vladas Pipiras , Barbara L. Fredrickson , Zachary F. Fisher This is my paper · ORCID
classification stat.ME MSC 62M1062H12
keywords discrete-valuedtimeseriesmultivariatelatentGaussianprocessYule–Walkerestimationanalyticstandarderrorscopula-styletransformintensivelongitudinaldata
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Discrete multivariate time series (counts, binary indicators, mixed types) lack a standard continuous-style toolkit, yet they are common in psychology, education, and related fields. The paper works with an existing copula-style construction that maps a latent stationary Gaussian vector process through deterministic quantile transforms so that each observed series can have its own prescribed marginal while the latent process carries a fully flexible autocorrelation structure. The new contribution is closed-form asymptotic standard errors for the Yule–Walker estimator of the latent VAR coefficients. The authors prove joint asymptotic normality of the marginal-parameter estimators and the observed autocovariances, then apply the delta method twice to obtain the limiting covariance of the latent dynamics. Simulation and an empirical daily diary example show that the resulting intervals achieve near-nominal coverage where a naïve Gaussian VAR applied directly to the discrete data systematically under-covers.

What carries the argument

The strictly increasing inverse-link map g = ℓ⁻¹ that recovers latent Gaussian autocovariances from observed autocovariances via a Hermite expansion of the copula-style transform; its analytic derivatives, composed with the Yule–Walker map, yield the sandwich form of Σ_Q.

What would settle it

In a Monte Carlo design with known latent VAR coefficients, check whether the analytic 95 percent intervals attain coverage near 0.95 once series length is moderate; systematic under-coverage that does not shrink with T would falsify the claimed limiting normality or the estimated Σ_Q.

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Extended reading notes

Core claim

The Yule–Walker estimator β̂ of the latent Gaussian VAR coefficients is jointly asymptotically normal: √T(β̂ − β) o d N(0, Σ_Q), where the limiting covariance Σ_Q is obtained in closed form from the joint asymptotics of the marginal-parameter estimators and the observed autocovariance matrices by two successive applications of the delta method.

Load-bearing premise

The spline approximation to the inverse link must return a positive-definite latent autocovariance matrix so that the Yule–Walker map stays well-defined and the implied process remains stationary.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The paper derives closed-form asymptotic standard errors for Yule–Walker estimators of the transition matrices of a latent Gaussian VAR that generates discrete-valued multivariate series via a copula-style Hermite transformation. It establishes joint asymptotic normality of the latent dynamics and marginal-parameter estimators through a multivariate CLT for stacked sample moments of the observed process, followed by two delta-method steps; an explicit first-order linearization of the Yule–Walker map appears in the Appendix (A3–A12), yielding the limiting covariance Σ_Q in (11). Finite-sample performance is examined in a large factorial Monte Carlo design (d ∈ {3,5}, T ∈ {50,100,200,500}, Bernoulli/Poisson/mixed margins; 36,000 series) and a mixed-type daily-diary application, with implementation in the open-source R package timecop.

Significance. Valid uncertainty quantification for latent-Gaussian discrete multivariate series has been missing from the estimation literature (Jia et al., 2023; Düker et al., 2024; Kim et al., 2025). If the asymptotics hold under the maintained causal-VAR and interior-correlation conditions, the paper supplies a practically usable tool for intensive longitudinal data with mixed discrete margins—precisely the setting common in psychology and education. Strengths include the carefully tracked delta-method linearization, the explicit form of Σ_Q, the factorial simulation with near-nominal coverage for T ≥ 200, honest discussion of nonstationary finite-sample failures, and a public software implementation. These are genuine contributions rather than incremental re-packaging.

major comments (2)
  1. Simulation Study, Nonstationary Solutions paragraph and Tables 1–3: Replications that produce non-positive-definite or ill-conditioned latent covariance matrices are discarded (or replaced by Higham projection). Because the abstract and results claim good performance of the analytic SEs and near-nominal coverage, the frequency of discarded replications by condition (d, T, margin type, parameter magnitude) must be reported. Without those rates, the Monte Carlo bias, RMSE, and coverage figures are conditional on admissible solutions and may overstate finite-sample reliability precisely where the paper notes the problem is most acute (short T, high d, boundary margins).
  2. Appendix (Assumptions L.1–L.4, V.1–V.3, M.1–M.4 referenced but deferred to Supplementary Materials): The central claim is asymptotic normality under regularity conditions that exclude boundary latent correlations and require a well-defined inverse-link map. A concise statement of the main assumptions (especially L.1 on interior correlations and the conditions that keep Γ̂_Z positive definite with probability tending to one) should appear in the main text or Appendix so that readers can assess applicability without the supplement. The asymptotic argument itself is standard and appears sound once those conditions are granted.
minor comments (6)
  1. Eq. (3) and surrounding text: Clarify the convention when Qi,n = ±∞ (summand set to 0) and give a practical truncation rule for the Hermite sum that was used in the simulations and package.
  2. Figures 1–4: Axis labels and legends are dense; consider separating absolute bias / relative bias / RMSE into panels with shared scales, or moving full tables to the main text and using figures only for coverage.
  3. Empirical Example, Table 4: Report the estimated marginal parameters (p̂, λ̂) and the estimated latent residual covariance so that readers can judge how far the series sit from the boundary cases flagged in the simulation.
  4. Discussion: The paragraph on distributional misspecification (overdispersion under a Poisson assumption) is important; a brief additional simulation or reference to robustness checks would strengthen the practical guidance.
  5. Notation: The switch between ΓZ(h) = RZ(h) (unit latent variances) and the later g• construction that forces diagonal entries to 1 is correct but easy to miss; a short remark near (A1)–(A2) would help.
  6. References: Andersson & Karlis (2025) is cited as arXiv; ensure the citation remains stable or update if a journal version appears before publication.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: asymptotic normality and closed-form SEs follow from a multivariate CLT on sample moments plus two ordinary delta-method steps; self-citations supply only the model definition, not the target limit law.

full rationale

The paper's central claim (Eq. 11) is that the Yule–Walker estimator of the latent Gaussian VAR coefficients is jointly asymptotically normal with an explicit limiting covariance Σ_Q. The derivation is self-contained: (i) a stacked moment process W_t that collects the estimating equations for the marginal parameters θ and the sample autocovariances of the observed series yields a multivariate CLT with long-run covariance Σ_Z (Newey–West estimable); (ii) the inverse-link map g and the Yule–Walker map are treated as fixed, continuously differentiable functions of (θ, Γ_X^{p+1}); (iii) two successive applications of the delta method, made explicit by the first-order linearization (A12) in the Appendix, produce Σ_Q. None of these steps defines the target quantity in terms of a free parameter that is later recovered, nor does any step invoke a uniqueness theorem or ansatz that is load-bearing only by self-citation. The self-citations (Jia et al. 2023, Düker et al. 2024, Kim et al. 2025) introduce the copula-style construction and the Hermite-link relation; they do not supply the normality or the SE formulas claimed here. Finite-sample non-positive-definiteness of the spline-based Γ̂_Z is acknowledged and handled by discarding or Higham projection, but those remedies affect only Monte-Carlo tables; under the paper's interior-correlation and stationarity assumptions the probability of such events vanishes asymptotically, so the limiting argument remains intact. Score 1 reflects only the ordinary presence of overlapping-author citations for background, not any circular reduction of the main result.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central asymptotic claim rests on standard CLT/delta-method machinery plus domain assumptions that the latent process is causal stationary Gaussian, the inverse-link map is continuously differentiable away from the boundary, and the marginal moment conditions identify the parameters. No free parameters are fitted to obtain the limiting covariance itself; the simulation merely evaluates finite-sample behavior under chosen designs. No new physical or mathematical entities are postulated.

assumptions (4)
  • domain assumption Latent process {Z_t} is a causal stationary Gaussian VAR(p) with unit marginal variances.
    Stated in Model Specification (Eq. 7) and used throughout the Yule-Walker asymptotics; required for the population map β = Γ^{-1}γ to be well-defined.
  • domain assumption Inverse link g_ij is continuously differentiable on the interior of its range and the Hermite coefficients satisfy the summability needed for the link derivative formula.
    Invoked for the first-order Taylor expansions (A5–A11) and the explicit derivative (16)–(17); boundary cases are excluded by Assumption L.1.
  • standard math Sample moments of the observed discrete process obey a multivariate CLT with long-run covariance Σ_Z that can be consistently estimated by HAC (Newey–West).
    Standard for strictly stationary weakly dependent series; used to obtain the joint normality of (θ̂, Γ̂_X) in (15).
  • domain assumption Marginal parameters θ are identified by moment conditions whose Jacobian is nonsingular.
    Required for the method-of-moments estimator θ̂ to be √T-consistent and for the stacked process W_t to have a non-degenerate covariance.

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Cite this review

Pith. "Pith review of Analytic Standard Errors for Latent Gaussian Discrete-Valued Multivariate Time Series." pith.science (2026). https://pith.science/paper/56XIRARX

@misc{pith2026260702732,
  author       = {Pith},
  title        = {Pith review of: Analytic Standard Errors for Latent Gaussian Discrete-Valued Multivariate Time Series},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/56XIRARX}},
  note         = {Machine review of arXiv:2607.02732}
}
read the original abstract

Unlike their continuous-valued counterparts, there are no universally preferred methodologies for modeling discrete-valued time series. This is especially problematic in fields such as psychology and education, where repeated-measures data often take the form of count, dichotomous, and ordered categorical variables. To address the need for flexible methodology for analyzing discrete-valued time series data, a copula-style multivariate model defined through deterministic functions of a latent stationary Gaussian vector series has been proposed. This model has several promising features, including the ability to accommodate a wide variety of marginal distributions within the same model while also allowing for the most flexible autocorrelation structure possible. We extend this framework by deriving analytic standard errors to facilitate inference on the latent Gaussian dynamics. In so doing, we establish the joint asymptotic normality of estimators of the parameters governing the latent Gaussian series and the marginal distributions. The performance of these analytic standard errors is examined in a simulation study and an empirical application.

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Works this paper leans on

95 extracted references · 23 canonical work pages

  1. [1]

    New Introduction to Multiple Time Series Analysis , year =

    Lütkepohl, Helmut , isbn =. New Introduction to Multiple Time Series Analysis , year =

  2. [2]

    Parent-child interaction: A micro-level sequential approach in children with a significant cognitive and motor developmental delay , volume=

    Van Keer, Ines and Ceulemans, Eva and Bodner, Nadja and Vandesande, Sien and Van Leeuwen, Karla and Maes, Bea , year=. Parent-child interaction: A micro-level sequential approach in children with a significant cognitive and motor developmental delay , volume=. doi:10.1016/j.ridd.2018.11.008 , journal=

    work page doi:10.1016/j.ridd.2018.11.008 2018

  3. [3]

    , volume=

    Pooled and person-specific machine learning models for predicting future alcohol consumption, craving, and wanting to drink: A demonstration of parallel utility. , volume=. Psychology of Addictive Behaviors , author=. 2022 , month=may, pages=. doi:10.1037/adb0000666 , number=

    work page doi:10.1037/adb0000666 2022

  4. [4]

    Counselling and Psychotherapy Research , author=

    Idiographic network analysis of discrete mood states prior to treatment , volume=. Counselling and Psychotherapy Research , author=. 2020 , month=sept, pages=. doi:10.1002/capr.12295 , number=

    work page doi:10.1002/capr.12295 2020

  5. [5]

    and Bosley, Hannah G

    Fisher, Aaron J. and Bosley, Hannah G. , year=. Identifying the presence and timing of discrete mood states prior to therapy , volume=. doi:10.1016/j.brat.2020.103596 , journal=

    doi:10.1016/j.brat.2020.103596 2020

  6. [6]

    Liu, Yang and Dora, Jonas and King, Kevin M. , year=. Daily self-control demands and loss of control over drinking: The moderating role of trait impulsivity and peer exposure , ISSN=. doi:10.1037/adb0001080 , journal=

    work page doi:10.1037/adb0001080

  7. [7]

    Personality and Social Psychology Bulletin , author=

    Studying Daily Social Interaction Quantity and Quality in Relation to Depression Change: A Multi-Phase Experience Sampling Study , volume=. Personality and Social Psychology Bulletin , author=. 2025 , month=july, pages=. doi:10.1177/01461672231211469 , number=

    work page doi:10.1177/01461672231211469 2025

  8. [8]

    and Gueorguieva, Ralitza and Taylor, Jane R

    DeMartini, Kelly S. and Gueorguieva, Ralitza and Taylor, Jane R. and Krishnan-Sarin, Suchitra and Pearlson, Godfrey and Krystal, John H. and O’Malley, Stephanie S. , year=. Dynamic structural equation modeling of the relationship between alcohol habit and drinking variability , volume=. doi:10.1016/j.drugalcdep.2021.109202 , journal=

    work page doi:10.1016/j.drugalcdep.2021.109202 2021

Show all 95 references
  1. [9]

    Examining Passively Collected Smartphone-Based Data in the Days Prior to Psychiatric Hospitalization for a Suicidal Crisis: Comparative Case Analysis , volume=

    Jacobucci, Ross and Ammerman, Brooke and Ram, Nilam , year=. Examining Passively Collected Smartphone-Based Data in the Days Prior to Psychiatric Hospitalization for a Suicidal Crisis: Comparative Case Analysis , volume=. doi:10.2196/55999 , journal=

    doi

  2. [10]

    Journal of Adolescent Research , author=

    Screenomics: A New Approach for Observing and Studying Individuals’ Digital Lives , volume=. Journal of Adolescent Research , author=. 2020 , month=jan, pages=. doi:10.1177/0743558419883362 , number=

    2020 doi

  3. [11]

    Journal of the Royal Statistical Society Series B: Statistical Methodology , author=

    Discrete Time Series Generated by Mixtures. Journal of the Royal Statistical Society Series B: Statistical Methodology , author=. 1978 , month=sept, pages=. doi:10.1111/j.2517-6161.1978.tb01653.x , number=

    1978 doi

  4. [12]

    Journal of the American Statistical Association , author=

    Count Time Series: A Methodological Review , volume=. Journal of the American Statistical Association , author=. 2021 , month=july, pages=. doi:10.1080/01621459.2021.1904957 , number=

    2021 doi

  5. [13]

    Journal of the American Statistical Association , author=

    Generalized Autoregressive Moving Average Models , volume=. Journal of the American Statistical Association , author=. 2003 , month=mar, pages=. doi:10.1198/016214503388619238 , number=

    2003 doi

  6. [14]

    Econometrics and Statistics , volume=

    Multivariate count time series modelling , author=. Econometrics and Statistics , volume=. 2024 , publisher=

    2024

  7. [15]

    Multivariate Behavioral Research , author=

    Bayesian Estimation of Categorical Dynamic Factor Models , volume=. Multivariate Behavioral Research , author=. 2007 , month=dec, pages=. doi:10.1080/00273170701715998 , number=

    2007 doi

  8. [16]

    Journal of Computational and Graphical Statistics , author=

    Generalized Dynamic Factor Models for Mixed-Measurement Time Series , volume=. Journal of Computational and Graphical Statistics , author=. 2014 , month=jan, pages=. doi:10.1080/10618600.2012.729986 , number=

    2014 doi

  9. [17]

    Scandinavian Journal of Statistics , author=

    Statistical Analysis of Time Series: Some Recent Developments , volume=. Scandinavian Journal of Statistics , author=. 1981 , pages=

    1981

  10. [18]

    Biometrika , author=

    A state space model for multivariate longitudinal count data , volume=. Biometrika , author=. 1999 , month=mar, pages=. doi:10.1093/biomet/86.1.169 , number=

    1999 doi

  11. [19]

    2008 , type =

    Van Rijn, Peter , title =. 2008 , type =

    2008

  12. [20]

    Journal of Business & Economic Statistics , author=

    Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity , volume=. Journal of Business & Economic Statistics , author=. 2011 , month=jan, pages=. doi:10.1198/jbes.2009.08212 , number=

    2011 doi arXiv

  13. [21]

    and Slipetz, Lindley R

    Henry, Teague R. and Slipetz, Lindley R. and Falk, Ami and Qiu, Jiaxing and Chen, Meng , year=. Ordinal Outcome State-Space Models for Intensive Longitudinal Data , ISSN=. doi:10.1007/s11336-024-09984-3 , journal=

    doi

  14. [22]

    Structural Equation Modeling: A Multidisciplinary Journal , author=

    Dynamic Structural Equation Models , volume=. Structural Equation Modeling: A Multidisciplinary Journal , author=. 2018 , month=may, pages=. doi:10.1080/10705511.2017.1406803 , number=

    2018 doi

  15. [23]

    Behavior Research Methods , author=

    Dynamic structural equation models with binary and ordinal outcomes in. Behavior Research Methods , author=. 2023 , month=apr, pages=. doi:10.3758/s13428-023-02107-3 , number=

    2023 doi

  16. [24]

    Journal of the American Statistical Association , author=

    Latent. Journal of the American Statistical Association , author=. 2023 , month=jan, pages=. doi:10.1080/01621459.2021.1944874 , number=

    2023 doi

  17. [25]

    and Pipiras, Vladas , title =

    Kim, Younghoon and Düker, Marie-Christine and Fisher, Zachary F. and Pipiras, Vladas , title =. Journal of Time Series Analysis , pages =. doi:10.1111/jtsa.70016 , year =

    doi

  18. [26]

    High-dimensional latent

    D. High-dimensional latent. Electronic Journal of Statistics , volume=. 2024 , publisher=

    2024

  19. [27]

    Approximating

    Nguyen, Quynh Nhu and De Oliveira, Victor , year=. Approximating. doi:10.1080/02664763.2025.2498502 , journal=

    2025 doi

  20. [28]

    Taqqu , title =

    Vladas Pipiras and Murad S. Taqqu , title =. 2017 , series =

    2017

  21. [29]

    Paul Gilbert and Ravi Varadhan , year =. num

  22. [30]

    2016 , note =

    cointReg: Parameter Estimation and Inference in a Cointegrating Regression , author =. 2016 , note =

    2016

  23. [31]

    Psychological Methods , author=

    When can categorical variables be treated as continuous? A comparison of robust continuous and categorical. Psychological Methods , author=. 2012 , month=sept, pages=. doi:10.1037/a0029315 , number=

    2012 doi

  24. [32]

    2008 , volume =

    Bernhard Pfaff , journal =. 2008 , volume =

    2008

  25. [33]

    PLoS ONE , author=

    A Network Approach to Psychopathology: New Insights into Clinical Longitudinal Data , volume=. PLoS ONE , author=. 2013 , month=apr, pages=. doi:10.1371/journal.pone.0060188 , number=

    2013 doi

  26. [34]

    Clinical Psychological Science , author=

    Emotion-Network Density in Major Depressive Disorder , volume=. Clinical Psychological Science , author=. 2015 , month=mar, pages=. doi:10.1177/2167702614540645 , number=

    2015 doi

  27. [35]

    Journal of Personality and Social Psychology , author=

    Consistency and change in idiographic personality: A longitudinal. Journal of Personality and Social Psychology , author=. 2020 , month=may, pages=. doi:10.1037/pspp0000249 , number=

    2020 doi

  28. [36]

    Mindfulness , author=

    Positive Emotion Correlates of Meditation Practice: a Comparison of Mindfulness Meditation and Loving-Kindness Meditation , volume=. Mindfulness , author=. 2017 , month=dec, pages=. doi:10.1007/s12671-017-0735-9 , number=

    2017 doi

  29. [37]

    , title =

    Fredrickson, Barbara L. , title =. Advances in Experimental Social Psychology , publisher =. 2013 , volume =

    2013

  30. [38]

    Journal of Computational and Graphical Statistics , author=

    Randomized Quantile Residuals , volume=. Journal of Computational and Graphical Statistics , author=. 1996 , month=sept, pages=. doi:10.1080/10618600.1996.10474708 , number=

    1996 doi

  31. [39]

    , title =

    Higham, Nicholas J. , title =. IMA Journal of Numerical Analysis , year =. doi:10.1093/imanum/22.3.329 , publisher =

    doi

  32. [40]

    Structural Equation Modeling: A Multidisciplinary Journal , author=

    Not Positive Definite Correlation Matrices in Exploratory Item Factor Analysis: Causes, Consequences and a Proposed Solution , volume=. Structural Equation Modeling: A Multidisciplinary Journal , author=. 2021 , month=jan, pages=. doi:10.1080/10705511.2020.1735393 , number=

    2021 doi

  33. [41]

    Maximum Likelihood Estimation of the

    Jonas Andersson and Dimitris Karlis , year=. Maximum Likelihood Estimation of the. 2512.00631 , archivePrefix=

  34. [42]

    , title =

    Kress, R. , title =. 1998 , volume =

    1998

  35. [43]

    Robust Covariance Matrix Estimation in Time Series: A Review , volume=

    Hirukawa, Masayuki , year=. Robust Covariance Matrix Estimation in Time Series: A Review , volume=. doi:10.1016/j.ecosta.2021.12.001 , journal=

    2021 doi

  36. [44]

    Psychology & Health , author=

    Same-day, cross-day, and upward spiral relations between positive affect and positive health behaviours , volume=. Psychology & Health , author=. 2021 , month=apr, pages=. doi:10.1080/08870446.2020.1778696 , number=

    2021 doi

  37. [45]

    Christopher Crawford and Younghoon Kim and Zachary Fisher and Vladas Pipiras and Marie Duker , year =

  38. [46]

    Electronic Journal of Statistics , volume=

    High-dimensional latent Gaussian count time series: Concentration results for autocovariances and applications , author=. Electronic Journal of Statistics , volume=. 2024 , publisher=

    2024

  39. [47]

    Frontiers in Applied Mathematics and Statistics , volume=

    On modeling a class of weakly stationary processes , author=. Frontiers in Applied Mathematics and Statistics , volume=. 2020 , publisher=

    2020

  40. [48]

    Frontiers in education , volume=

    Why ordinal variables can (almost) always be treated as continuous variables: Clarifying assumptions of robust continuous and ordinal factor analysis estimation methods , author=. Frontiers in education , volume=. 2020 , organization=

    2020

  41. [49]

    Journal of Research in Personality , volume=

    Intraindividual differences dimensions of mood change during pregnancy identified in five P-technique factor analyses , author=. Journal of Research in Personality , volume=. 1978 , publisher=

    1978

  42. [50]

    Journal of Statistical Software , volume=

    lavaan: An R package for structural equation modeling , author=. Journal of Statistical Software , volume=

  43. [51]

    The Annals of Statistics , number =

    Sjoerd Dirksen and Johannes Maly and Holger Rauhut , title =. The Annals of Statistics , number =

  44. [52]

    High-dimensional mixed graphical model with ordinal data: Parameter estimation and statistical inference , year =

    Feng, Huijie and Ning, Yang , booktitle=. High-dimensional mixed graphical model with ordinal data: Parameter estimation and statistical inference , year =

  45. [53]

    Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data , volume =

    Fernando, Dimuthu and Alqawba, Mohammed and Samad, Manar and Diawara, Norou , journal =. Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data , volume =

  46. [54]

    Some autoregressive moving average processes with generalized

    Alzaid, Abdulhamid A and Al-Osh, Mohamed A , journal =. Some autoregressive moving average processes with generalized

  47. [55]

    Some simple models for discrete variate time series , volume =

    McKenzie, Ed , journal =. Some simple models for discrete variate time series , volume =

  48. [56]

    Handbook of discrete-valued time series , year =

    Davis, Richard A and Holan, Scott H and Lund, Robert and Ravishanker, Nalini , publisher =. Handbook of discrete-valued time series , year =

  49. [57]

    Gamerman, Dani and Abanto-Valle, Carlos A and Silva, Ralph S and Martins, Thiago G and Davis, RA and Holan, SH and Lund, R and Ravishanker, N , journal =. Dynamic

  50. [58]

    Integer-valued

    Ferland, Ren. Integer-valued. Journal of Time Series Analysis , number =

  51. [59]

    Poisson autoregression , volume =

    Fokianos, Konstantinos and Rahbek, Anders and Tj. Poisson autoregression , volume =. Journal of the American Statistical Association , number =

  52. [60]

    Models for multivariate count time series , volume =

    Karlis, Dimitris , journal =. Models for multivariate count time series , volume =

  53. [61]

    Modeling Multiple-Subject and Discrete-Valued High-Dimensional Time Series , year =

    Kim, Younghoon , journal =. Modeling Multiple-Subject and Discrete-Valued High-Dimensional Time Series , year =

  54. [62]

    Seasonal count time series , volume =

    Kong, Jiajie and Lund, Robert , journal =. Seasonal count time series , volume =

  55. [63]

    , publisher =

    Vershynin, R. , publisher =. Lectures in Geometric Functional Analysis , year =

  56. [64]

    Adaptive estimation of the copula correlation matrix for semiparametric elliptical copulas , volume =

    Wegkamp, Marten and Zhao, Yue , journal =. Adaptive estimation of the copula correlation matrix for semiparametric elliptical copulas , volume =

  57. [65]

    James Livsey and Robert Lund and Stefanos Kechagias and Vladas Pipiras , journal =

  58. [66]

    Jia, Yisu and Kechagias, Stefanos and Livsey, James and Lund, Robert and Pipiras, Vladas , journal =. Latent

  59. [67]

    The spectrum of clipped noise , volume =

    Van Vleck, John H and Middleton, David , journal =. The spectrum of clipped noise , volume =

  60. [68]

    and Fisher, Zachary F and Pipiras, Vladas , journal =

    Kim, Younghoon and D\"uker, M.-C. and Fisher, Zachary F and Pipiras, Vladas , journal =. Latent Gaussian dynamic factor modeling and forecasting for high-dimensional count time series , year =

  61. [69]

    Psychometrika , volume=

    Penalized estimation and forecasting of multiple subject intensive longitudinal data , author=. Psychometrika , volume=. 2022 , publisher=

    2022

  62. [70]

    Count time series:

    Davis, Richard A and Fokianos, Konstantinos and Holan, Scott H and Joe, Harry and Livsey, James and Lund, Robert and Pipiras, Vladas and Ravishanker, Nalini , journal =. Count time series:

  63. [71]

    Horn, R. A. and Johnson, C. R. , publisher =. Topics in Matrix Analysis , year =

  64. [72]

    Horn, R. A. and Johnson, C. R. , publisher =. Matrix Analysis , year =

  65. [73]

    Long-range Dependence and Self-Similarity , volume =

    Pipiras, Vladas and Taqqu, Murad S , publisher =. Long-range Dependence and Self-Similarity , volume =

  66. [74]

    Estimation in high-dimensional vector autoregressive models , volume =

    Basu, Sumanta and Michailidis, George , journal =. Estimation in high-dimensional vector autoregressive models , volume =

  67. [75]

    Baek, Changryong and D. Local. The Annals of Statistics , volume=. 2023 , publisher=

    2023

  68. [76]

    Regularized estimation in sparse high-dimensional time series models , volume =

    Basu, Sumanta and Michailidis, George , journal =. Regularized estimation in sparse high-dimensional time series models , volume =

  69. [77]

    High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity , volume =

    Loh, Po-Ling and Wainwright, Martin J , journal =. High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity , volume =

  70. [78]

    and Neudecker, H

    Magnus, J. and Neudecker, H. , publisher =. Matrix Differential Calculus with Applications in Statistics and Econometrics , year =

  71. [79]

    Hoeffding's Inequality for General

    Fan, Jianqing and Jiang, Bai and Sun, Qiang , journal =. Hoeffding's Inequality for General

  72. [80]

    An, H. Z. and Huang, F. C. , journal =. The geometrical ergodicity of nonlinear autoregressive models , volume =

  73. [81]

    Latent association mining in binary data , year =

    Mosso, Carson and Bodwin, Kelly and Chakraborty, Suman and Zhang, Kai and Nobel, Andrew B , journal =. Latent association mining in binary data , year =

  74. [82]

    High-dimensional semiparametric

    Liu, Han and Han, Fang and Yuan, Ming and Lafferty, John and Wasserman, Larry , journal =. High-dimensional semiparametric

  75. [83]

    Multivariate analysis of nonparametric estimates of large correlation matrices , year =

    Mitra, Ritwik and Zhang, Cun-Hui , journal =. Multivariate analysis of nonparametric estimates of large correlation matrices , year =

  76. [84]

    Semiparametric

    Segers, Johan and Van den Akker, Ramon and Werker, Bas JM , journal =. Semiparametric

  77. [85]

    Geometric ergodicity and hybrid

    Roberts, Gareth and Rosenthal, Jeffrey , journal =. Geometric ergodicity and hybrid

  78. [86]

    A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators , volume =

    Muth. A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators , volume =. Psychometrika , number =

  79. [87]

    Structural equation models with continuous and polytomous variables , volume =

    Lee, Sik-Yum and Poon, Wai-Yin and Bentler, Peter M , journal =. Structural equation models with continuous and polytomous variables , volume =

  80. [88]

    Mplus 7.11 , year =

    Muth. Mplus 7.11 , year =. Los Angeles, CA: Muth

  81. [89]

    Exponential concentration inequalities for additive functionals of

    Adamczak, Rados. Exponential concentration inequalities for additive functionals of. ESAIM: Probability and Statistics , pages =

  82. [90]

    Concentration inequalities for empirical processes of linear time series

    Chen, Likai and Wu, Wei Biao , journal =. Concentration inequalities for empirical processes of linear time series. , volume =

  83. [91]

    Concentration inequalities for non-

    Adamczak, Rados. Concentration inequalities for non-. Probability Theory and Related Fields , number =

  84. [92]

    Fisher, and Vladas Pipiras , journal =

    Younghoon Kim, Zachary F. Fisher, and Vladas Pipiras , journal =. Latent

  85. [93]

    Fang Han and Han Liu , journal =

  86. [94]

    High dimensional semiparametric latent graphical model for mixed data , volume =

    Fan, Jianqing and Liu, Han and Ning, Yang and Zou, Hui , journal =. High dimensional semiparametric latent graphical model for mixed data , volume =

  87. [95]

    Biometrika , pages=

    The Equivalence of Tetrachoric and Maximum Likelihood Estimates of in 2 2 Tables , author=. Biometrika , pages=. 1970 , publisher=

    1970

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Reviewed July 12, 2026 · model on record in the stance chip above.