Pith. sign in

REVIEW 4 major objections 4 minor 40 references

The paper argues that high-dimensional mean-change tests and localization remain valid under temporal dependence by pairing quadratic and coordinatewise-maximum CUSUM scans.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 09:17 UTC pith:FKU62FH2

load-bearing objection Real and substantial framework for sparsity-adaptive change-point inference under temporal dependence, but the load-bearing Assumption 3 can fail for a simple sub-Gaussian process, so the advertised 'general non-Gaussian' coverage is not supported. the 4 major comments →

arxiv 2607.20828 v1 pith:FKU62FH2 submitted 2026-07-23 stat.ME

High-Dimensional Change Point Analysis for Temporally Dependent Data

Xiaoyi Wang , Le Zhou , Jixuan Liu , Long Feng This is my paper
classification stat.ME MSC 62M1062H1562G20
keywords change point detectionhigh-dimensional time seriesCUSUM statisticsCauchy combination testlong-run covariancewild binary segmentationtemporal dependencesparsity adaptation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper sets out to prove that detecting and locating a mean change in a high-dimensional time series does not require temporal independence or Gaussianity. It pairs two scans — a quadratic CUSUM that aggregates evidence across all coordinates (for dense changes) and a coordinatewise maximum CUSUM (for sparse changes) — and recalibrates both for serial dependence using long-run covariance estimates and dependence-adjusted centering. Its central result is that matched quadratic and maximum scans are asymptotically independent under the null, so combining them through a Cauchy test preserves size while adapting to unknown sparsity. The paper also proves consistency and rates for single-change localization and, via guarded wild binary segmentation, consistent recovery of multiple changes. If correct, this gives practitioners one set of procedures for testing, dating, and enumerating changes in dependent high-dimensional panels.

Core claim

The paper's central claim is that, under non-Gaussian vector dependence with sub-Gaussian projections and a higher-order connected-cumulant contraction condition, the feasible quadratic CUSUM path converges to a Gaussian process with supremum distribution F_V, the boundary-weighted quadratic and both maximum scans converge to Gumbel limits after Darling–Erdős normalization, and matched quadratic/maximum pairs are asymptotically independent — for instance Pr{S0 <= x, 2M0^2 − log(2p) <= y} -> F_V(x)F_Gumbel(y). Those independence facts justify Cauchy-combination tests that adapt to dense or sparse alternatives. The same centered scores localize a single change with explicit rates, and a guarde

What carries the argument

The load-bearing object is the matched pair of CUSUM scans: the quadratic statistic W(k), centered by a dependence-adjusted mean and scaled by a long-run scale that keeps the two trace orientations tr{Gamma(h)Gamma(k)^T} and tr{Gamma(h)Gamma(k)} separate; and the coordinatewise maximum M, standardized by difference-based long-run marginal variance estimates. Two temporal weightings (gamma=0 unweighted, gamma=1/2 variance-standardized) are paired. The asymptotic independence of a matched pair — with the F_V supremum limit for the unweighted quadratic path and Gumbel limits for the max and boundary-weighted paths — is the mechanism that legitimizes the Cauchy combination. Wild binary segmentat

Load-bearing premise

The load-bearing premise is Assumption 3: sums of higher-order temporal cumulant blocks must grow only linearly in dimension, and no primitive data-checkable condition is given for it (with a secondary constraint that boundary-weighted theorems need p growing faster than (log n)^4, which the paper's simulations do not meet).

What would settle it

Simulate a stationary non-Gaussian vector MA(2) with heavy-tailed innovations at n=800, p=250, estimate the connected cumulant sums in Assumption 3 from the residuals, and compare the empirical null distribution of S0 and S_{1/2} with the claimed F_V and Gumbel limits. If those cumulant sums are not O(p), or if the empirical sizes deviate from the nominal level once the assumed growth rates (e.g., p >> (log n)^4) are violated, the central claim fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Cauchy-combined tests are asymptotically size-valid under serial dependence for both dense and sparse alternatives, without knowing sparsity in advance.
  • For a detected change, the adaptive estimator chooses the dense or sparse localizer by component p-values and is consistent whenever one component is consistent.
  • Guarded wild binary segmentation consistently estimates the number of change points and attains localization rates, with estimated locations converging relative to the minimum spacing.
  • The variance-standardized boundary-weighted scans have a Gumbel null limit, so near-boundary changes can be detected and localized without simulating a new reference distribution.
  • Ignoring serial dependence in these settings is not harmless: the paper's simulations show independence-calibrated procedures reject in nearly every replication under an MA(2) design.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • As a reader inference, the boundary-weighted calibration is proven only when p grows faster than (log n)^4; with n=789 and p=119 (the macro application), log n ≈ 6.7 exceeds p^{1/4} ≈ 3.3, so that reported accuracy is an empirical demonstration outside the proven regime rather than a theorem consequence.
  • As a reader inference, the finite-sample Gamma tail corrections and preprocessing used in the implementation are not invoked in the formal proofs; comparing them to the asymptotic Gumbel calibration at small p would directly measure how much of the size control is proof versus calibration.
  • As a reader inference, the dense and sparse components often select different dates in the empirical panels, suggesting the matched scans can be read as a decomposition of a change into broad shifts and concentrated shifts — a use the paper mentions but does not formalize.
  • As a reader inference, a natural extension, pointed to by the paper's own outlook, is a diverging number of changes with shrinking spacing; the fixed-proportion spacing assumption in the WBS theorems is what keeps the shortest-significant selection valid.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper proposes sparsity-adaptive tests and localizers for a high-dimensional mean change under temporal dependence. It pairs a quadratic CUSUM scan (dense signal) with a coordinatewise maximum CUSUM scan (sparse signal), under two temporal weightings: an unweighted full scan and a variance-standardized trimmed scan. For each statistic the authors introduce dependence-adjusted centering and long-run scale estimation, prove Gaussian-process or Gumbel null limits, and prove asymptotic independence of the matched quadratic and maximum statistics, which justifies Cauchy combination tests. They also prove single-change localization rates and consistent multiple-change recovery via guarded wild binary segmentation. The paper includes an extensive supplement, simulations for Gaussian and standardized Gamma innovations, and applications to FRED-MD and electricity-load panels.

Significance. If correct, the paper would fill a real gap: joint null calibration of dense and sparse CUSUM scans under non-Gaussian temporal dependence, plus localization and multiple-change recovery within one framework. The supplement is unusually detailed and the simulations are honestly reported, including the explicit concession that the Gamma design lies outside Assumption 1 and the post-hoc white-noise diagnostics showing remaining dependence after mean removal. However, the central "general non-Gaussian" claim rests on Assumption 3, which is not implied by Assumptions 1–2 and fails for a simple temporally independent sub-Gaussian process. In addition, the rate in Theorem 2 contains an impossible term, and the boundary-weighted results are only proved under a growth condition violated by every simulation and application. These issues are load-bearing; the manuscript needs substantial revision before its main claims can be accepted.

major comments (4)
  1. [Assumption 3 and Lemmas S.3–S.5, S.19, S.24] Assumption 3 is the hinge for the Gaussian comparison steps that produce Theorem 1, Theorem 5, and the WBS theorems, but it is not a consequence of Assumptions 1–2 and it can fail inside the stated framework. Let f_t be iid uniform on [-sqrt(3), sqrt(3)], let eta_{t,j} be iid Rademacher, and set eps_{t,j}=f_t eta_{t,j}. This process is m=0-dependent, projection sub-Gaussian, has Omega=I, and satisfies Assumption 4. For the connected single-block partition in q=2, the blockwise cumulant envelope gives C_{pi,p} = (3/4)p(p-1) - (6/5)p = (3/4)p^2 - (27/20)p = O(p^2), violating Assumption 3. Thus the central theorem's hypotheses are not satisfied by a simple iid sub-Gaussian process, and the claim of covering "general non-Gaussian" dependence is unsupported. The paper gives no primitive sufficient conditions for Assumption 3, and the simulations provide no non-Gaussian evidence: the Gaussian
  2. [Theorem 2, definition of r_mu,n] The theorem defines r_mu,n = M*sqrt(n) + sqrt(p) M eta_M + ... and asserts r_mu,n -> 0. With M = ceil((n ^ p)^{1/8}), the leading term M*sqrt(n) diverges for every sequence satisfying p = o(n^{3/2}): if p >= n it is at least n^{5/8}, and if p is fixed it is order n^{1/2}. Therefore the stated uniform centering rate cannot be negligible, and the subsequent uses of r_mu,n in Theorem 3 and Theorem 5 are not justified. The proof of Lemma S.10 obtains a stochastic contribution of order M/sqrt(n), so it appears that M/sqrt(n) was intended. If so, correct Theorem 2 and re-verify the feasibility conditions in Theorems 3 and 5; otherwise prove the displayed rate or revise the statement.
  3. [Theorem 3(ii), Theorem 5, and Section 6/7.1] The boundary-weighted asymptotic statements require log n = o(p^{1/4}). This condition is violated in every simulation and in the FRED-MD application: for n=789, p=119, log n is about 6.67 while p^{1/4} is about 3.30; similarly, n=400, p=250 gives log n ~ 5.99 versus p^{1/4} ~ 3.98, and n=800, p=500 gives 6.68 versus 4.73. Since the boundary-weighted statistics S_{1/2}, M_{1/2}, and T_{CC,1/2} are used and reported as decisive in the applications, the paper is exercising its main calibration tools outside the proven regime. Please either add simulations and applications that satisfy the stated growth condition, or establish the boundary-weighted limits under less restrictive conditions.
  4. [Simulation Section 6: non-Gaussian coverage of Assumption 3] The only non-Gaussian simulation design is the standardized Gamma innovation, which the paper itself places outside Assumption 1. Thus no simulation demonstrates that Assumption 3 is satisfiable by a non-Gaussian process or that the Gaussian comparison bounds hold beyond the Gaussian-filter case. The empirical size and power results are informative as finite-sample illustrations, but they should not be read as evidence for the general non-Gaussian theorem. Please provide a non-Gaussian simulation within Assumptions 1–3, or state clearly that Assumption 3 is not numerically verified.
minor comments (4)
  1. [Theorem 2 notation] The term M*sqrt(n) in r_mu,n appears to be a typo for M/sqrt(n). The proof and the claimed convergence suggest the latter; please fix the display and check all places where r_mu,n is used.
  2. [Sections 2 and 6: Gamma design disclaimer] The statement that the standardized Gamma design is outside Assumption 1 is honest, but the text later says the procedures "retain their sparsity-adaptive behavior under the asymmetric non-Gaussian design." That is a finite-sample claim, not a validation of Theorems 1–5; please make this distinction explicit in the simulation discussion.
  3. [Section 3 and Section 7: calibration implementation] The RCP preprocessing and finite-LRV tail formulas are described as finite-sample calibration choices not covered by the formal theorems, yet the reported p-values in the applications use them. This is acceptable if clearly labeled, but please add a sentence reminding the reader that the formal theorems apply to the asymptotic p-values, not to the implemented p_FLRV versions.
  4. [General presentation] The supplement is very long and dense, with many locally defined objects. Adding a short table of notation, especially for the many superscripts on Gaussian analogues (M^{G,gamma}, M^{B,gamma}, M^{eps,gamma}) and for the multiple-change rates, would substantially improve readability.

Circularity Check

0 steps flagged

No significant circularity: the limiting laws are derived from explicit assumptions; the only self-citation is a published Gaussian-extreme-value theorem used as a tool, not a reduction of the target result to its inputs.

full rationale

The central derivation is conditional on explicit assumptions (Assumptions 1–4) and proves the Gaussian-process, Gumbel, and joint limits via Gaussian comparison, cumulant bounds, and decoupling. The limit covariance of V is obtained from 2 K_B^2 tr(Omega^2)/p after scaling by omega_p, so the law of V is a derived limiting object, not an input or a fitted quantity. The simulated F_V in Remark 1 evaluates that derived covariance, and the Gumbel calibrations are the corresponding limiting distributions. Feasible centering and orientation-complete scaling are proved consistent in Theorem 2; the CF2 correction is proved to be an asymptotically negligible remainder (Lemma S.12), not a fitted correction. The finite-sample LRV tail formulas are explicitly described as computational calibration choices that are not used in the proofs of Theorem 4 or the independence theorems. The closest thing to a self-referential step is the reliance on Wang and Feng (2023) for the Gaussian extreme-value limit and the factorial-moment decoupling argument used in Lemmas S.13 and S.15. Because Wang and Feng is a published theorem on Gaussian processes under Assumption 4-type correlation conditions, and because the present paper records and verifies the relevant decoupling calculation in the supplement, this citation is legitimate independent support rather than a circular reduction to the paper's own conclusion. The more serious concern is that Assumption 3 is a high-level connected-cumulant condition not shown to follow from Assumptions 1–2, and the standardized Gamma design is explicitly outside Assumption 1; that is a coverage and robustness gap, not a circularity in the derivation chain.

Axiom & Free-Parameter Ledger

4 free parameters · 7 axioms · 0 invented entities

The central claims rest on four domain assumptions about the error process (sub-Gaussian projections, bounded long-run spectrum, cumulant contraction bounds, weak cross-sectional correlation), a fixed-proportion spacing assumption for multiple changes, and the paper's own tuning feasibility condition. Free parameters are standard tuning choices (trimming, lag truncation, LRV bandwidth, WBS settings); none is fitted to the target data, but the LRV bandwidth rule and the empirical WBS settings are not fully specified, which limits reproducibility.

free parameters (4)
  • lambda_n (boundary trimming) = floor(sqrt(n)) in experiments; theory allows lambda_n ~ n^lambda for any lambda in (0,1)
    Controls the trimmed candidate set K_{1/2} for variance-standardized scans; enters the logit scan-window length log h_n and all gamma=1/2 conditions.
  • M (lag truncation for centering/scale) = ceil((n∧p)^{1/8})
    Truncation lag for the dependence-adjusted centering and long-run scale estimators; appears in every rate and signal condition in Theorems 1-9.
  • LRV bandwidth ell_j = data-driven; selection rule not specified
    Bandwidth for the third-difference long-run variance estimator; theory requires ell_min -> infinity, ell_max = o(sqrt(n)), and ell_j ~ n^{1/(1+2q)} for rates, but the exact data-driven rule used in the implementation is not given.
  • WBS tuning: ell_W,n, N_W,n, d_W,n, Lambda_W = simulations: 300 intervals, min length 20, guard 95, threshold n^{1/4}; applications unspecified
    Minimum interval length, number of random intervals, separation guard, and component thresholds in wild binary segmentation; Assumption 6 gives feasible ranges, but the empirical application values are not reported.
axioms (7)
  • domain assumption Assumption 1: projection sub-Gaussianity plus one of strong mixing (AM), fixed m-dependence (MD), or physical dependence (PD)
    Restricts the error process: every unit-variance linear projection must have sub-Gaussian tails. Excludes heavy-tailed and sub-exponential processes; Section 6 concedes the standardized Gamma(4,1) design lies outside it.
  • domain assumption Assumption 2: bounded long-run spectrum with p^{-1}tr(Omega^2) -> theta_Omega in (0,infinity) and inf_lambda p^{-1}tr(f_p(lambda)) >= c_f
    Requires no dominant long-run direction and positive average spectral mass at all frequencies; needed for the Gaussian-process limit of the quadratic scan and fails for factor-dominated panels.
  • domain assumption Assumption 3: connected cumulant contractions max_pi C_{pi,p} <= C_q p for q = 2,3,4
    The most opaque load-bearing condition: bounds 4th-8th order joint cumulants of the quadratic CUSUM; underlies Lemmas S.3-S.5, S.19, S.24. No primitive sufficient conditions are proved beyond Gaussian pairings and finite-order filters.
  • domain assumption Assumption 4: weak long-run cross-sectional dependence (|rho_jj'| <= rho < 1, sparse near-neighborhood)
    Needed for the Gaussian extreme-value limit of the coordinatewise max statistics and for the asymptotic-independence decoupling argument.
  • domain assumption Assumption 5: fixed K_cp, Delta_n >= c_Delta n, bounded jumps
    Multiple changes must be fixed in number and proportionally separated; the paper acknowledges in Section 8 that it excludes diverging numbers and shrinking spacing.
  • ad hoc to paper Assumption 6: WBS feasibility tuning (ell_W,n, N_W,n, d_W,n, bandwidths)
    Constrains the method's own tuning parameters so Theorems 8-9 hold; the paper shows the constraints are nonempty in a polynomial regime.
  • standard math Gaussian comparison and extreme-value background (Chernozhukov-Chetverikov-Kato 2013/2017, Leadbetter et al. 1983, Leonov-Shiryaev 1959, Tsirelson 1976, Moricz 1982)
    Background results invoked throughout the supplement: Gaussian approximation, cumulant factorizations, supremum density, maximal inequalities, extreme-value limits.

pith-pipeline@v1.3.0-alltime-deepseek · 90580 in / 29681 out tokens · 295743 ms · 2026-08-01T09:17:38.767848+00:00 · methodology

0 comments
read the original abstract

This paper develops adaptive procedures for detecting and locating mean changes in high-dimensional time series. Quadratic CUSUM statistics target dense changes, whereas coordinatewise maximum statistics target sparse changes. Two weighting schemes are considered to accommodate both interior and boundary changes. Under general non-Gaussian vector dependence, we establish the limiting distributions, validate the required centering and scaling estimators, and prove asymptotic independence between matched quadratic and maximum statistics. These results justify Cauchy combination tests. We further establish single-change localization and consistent multiple-change recovery using wild binary segmentation. Numerical results illustrate the effectiveness of the proposed methods.

Figures

Figures reproduced from arXiv: 2607.20828 by Jixuan Liu, Le Zhou, Long Feng, Xiaoyi Wang.

Figure 1
Figure 1. Figure 1: Empirical power under Scenario (S2), 𝑞MA = 2, and 𝜏 = 0.3𝑛. The left and right panels correspond to normal and standardized Gamma(4, 1) innovations, respectively. Figures 1–2 report the empirical rejection probabilities for the two change-point locations. Under the stated calibration, ∥𝜹∥ 2 2 = 𝑠𝛿2 1 = 𝑐 2 𝜏 log 𝑝 𝑛 , so the aggregate squared signal remains fixed as 𝑠 increases, whereas the magnitude of ea… view at source ↗
Figure 2
Figure 2. Figure 2: Empirical power under Scenario (S2), 𝑞MA = 2, and 𝜏 = 0.5𝑛. The left and right panels correspond to normal and standardized Gamma(4, 1) innovations, respectively. become preferable after the transition from sparse to dense alternatives. This complementary behavior is observed for both change-point locations and under both innovation distributions. The two Cauchy combinations adapt to this transition. For s… view at source ↗
Figure 3
Figure 3. Figure 3: Average normalized absolute localization error under Scenario (S2), [PITH_FULL_IMAGE:figures/full_fig_p025_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Average normalized absolute localization error under Scenario (S2), [PITH_FULL_IMAGE:figures/full_fig_p025_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Multiple-change localization under Scenario (S2), [PITH_FULL_IMAGE:figures/full_fig_p027_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Estimated multiple change points for the FRED-MD panel. Circles and triangles denote [PITH_FULL_IMAGE:figures/full_fig_p029_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Estimated multiple change points for the Electricity Load Diagrams panel under the conservative [PITH_FULL_IMAGE:figures/full_fig_p031_7.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

40 extracted references · 2 linked inside Pith

  1. [1]

    Adler, R. J. and J. E. Taylor (2007).Random Fields and Geometry. Springer

    2007

  2. [2]

    Aston, J. A. D. and C. Kirch (2018). High dimensional efficiency with applications to change point tests.Electronic Journal of Statistics 12(1), 1901–1947

    2018

  3. [3]

    Bai, J. (2010). Common breaks in means and variances for panel data.Journal of Econometrics 157(1), 78–92

    2010

  4. [4]

    Chen, and P

    Baranowski, R., Y. Chen, and P. Fryzlewicz (2019). Narrowest-over-threshold detection of multiple change points and change-point-like features.Journal of the Royal Statistical Society: Series B (Statistical Methodology) 81(3), 649–672

    2019

  5. [5]

    (2013).Convergence of Probability Measures

    Billingsley, P. (2013).Convergence of Probability Measures. Wiley

    2013

  6. [6]

    Chan, K. W. (2022). Optimal difference-based variance estimators in time series: A general framework.The Annals of Statistics 50(3), 1376–1400

    2022

  7. [7]

    Chen, and M

    Chang, J., X. Chen, and M. Wu (2024). Central limit theorems for high dimensional dependent data.Bernoulli 30(1), 712–742

    2024

  8. [8]

    Chang, J., J. He, C. Lin, and Q. Yao (2024). HDTSA: An R package for high-dimensional time series analysis. arXiv preprint arXiv:2412.17341

    Pith/arXiv arXiv 2024

  9. [9]

    Wang, and W

    Chen, L., W. Wang, and W. B. Wu (2022). Inference of breakpoints in high-dimensional time series.Journal of the American Statistical Association 117(540), 1951–1963

    2022

  10. [10]

    Chetverikov, and K

    Chernozhukov, V., D. Chetverikov, and K. Kato (2013). Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors.The Annals of Statistics 41(6), 2786–2819

    2013

  11. [11]

    Chetverikov, and K

    Chernozhukov, V., D. Chetverikov, and K. Kato (2017). Central limit theorems and bootstrap in high dimensions. The Annals of Probability 45(4), 2309–2352

    2017

  12. [12]

    Cho, H. (2016). Change-point detection in panel data via double CUSUM statistic.Electronic Journal of Statistics 10(2), 2000–2038

    2016

  13. [13]

    Davydov, Y. A. (1968). Convergence of distributions generated by stationary stochastic processes.Theory of Probability and Its Applications 13(4), 691–696

    1968

  14. [14]

    Enikeeva, F. and Z. Harchaoui (2019). High-dimensional change-point detection under sparse alternatives.The Annals of Statistics 47(4), 2051–2079

    2019

  15. [15]

    Fryzlewicz, P. (2014). Wild binary segmentation for multiple change-point detection.The Annals of Statistics 42(6), 2243–2281. Horv´ath, L. and M. Huˇskov´a (2012). Change-point detection in panel data.Journal of Time Series Analysis 33(4), 631–648

    2014

  16. [16]

    (1997).Gaussian Hilbert Spaces

    Janson, S. (1997).Gaussian Hilbert Spaces. Cambridge: Cambridge University Press

    1997

  17. [17]

    Jin, B., G. Pan, Q. Yang, and W. Zhou (2016). On high-dimensional change point problem.Science China Mathematics 59(12), 2355–2378

    2016

  18. [18]

    Jirak, M. (2015). Uniform change point tests in high dimension.The Annals of Statistics 43(6), 2451–2483

    2015

  19. [19]

    Leadbetter, M. R., G. Lindgren, and H. Rootz ´en (1983).Extremes and Related Properties of Random Sequences and Processes. New York: Springer

    1983

  20. [20]

    Leonov, V. P. and A. N. Shiryaev (1959). On a method of calculation of semi-invariants.Theory of Probability and Its Applications 4(3), 319–329

    1959

  21. [21]

    Xu, P.-S

    Li, J., M. Xu, P.-S. Zhong, and L. Li (2019). Change point detection in the mean of high-dimensional time series data under dependence.arXiv preprint arXiv:1903.07006. 105

    Pith/arXiv arXiv 2019

  22. [22]

    Zhang, and Y

    Liu, B., X. Zhang, and Y. Liu (2022). High dimensional change point inference: Recent developments and extensions.Journal of Multivariate Analysis 188, 104833

    2022

  23. [23]

    Liu, B., C. Zhou, X. Zhang, and Y. Liu (2020). A unified data-adaptive framework for high dimensional change point detection.Journal of the Royal Statistical Society: Series B 82(4), 933–963

    2020

  24. [24]

    Gao, and R

    Liu, H., C. Gao, and R. J. Samworth (2021). Minimax rates in sparse, high-dimensional change point detection. The Annals of Statistics 49(2), 1081–1112

    2021

  25. [25]

    McCracken, M. W. and S. Ng (2016). FRED-MD: A monthly database for macroeconomic research.Journal of Business & Economic Statistics 34(4), 574–589

    2016

  26. [26]

    Peligrad, and E

    Merlev`ede, F., M. Peligrad, and E. Rio (2011). A bernstein type inequality and moderate deviations for weakly dependent sequences.Probability Theory and Related Fields 151(3–4), 435–474. M´oricz, F. (1982). A general moment inequality for the maximum of partial sums of single series.Acta Scientiarum Mathematicarum 44(1–2), 67–75

    2011

  27. [27]

    Carpentier, and N

    Pilliat, E., A. Carpentier, and N. Verzelen (2023). Optimal multiple change-point detection for high-dimensional data.Electronic Journal of Statistics 17(1), 1240–1315

    2023

  28. [28]

    Saulis, L. and V. A. Statuleviˇcius (1991).Limit Theorems for Large Deviations. Dordrecht: Springer

    1991

  29. [29]

    Trindade, A. (2015). ElectricityLoadDiagrams20112014. UCI Machine Learning Repository. Dataset

    2015

  30. [30]

    Tsirelson, V. S. (1976). The density of the distribution of the maximum of a gaussian process.Theory of Probability and Its Applications 20(4), 847–856

    1976

  31. [31]

    Wang, G. and L. Feng (2023). Computationally efficient and data-adaptive changepoint inference in high dimension. Journal of the Royal Statistical Society: Series B 85(3), 936–958

    2023

  32. [32]

    Zou, and G

    Wang, G., C. Zou, and G. Yin (2018). Change-point detection in multinomial data with a large number of categories.The Annals of Statistics 46(5), 2020–2044

    2018

  33. [33]

    Wang, R. and X. Shao (2023). Dating the break in high-dimensional data.Bernoulli 29(4), 2879–2901

    2023

  34. [34]

    Wang, R., C. Zhu, S. Volgushev, and X. Shao (2022). Inference for change points in high-dimensional data via self-normalization.The Annals of Statistics 50(2), 781–806

    2022

  35. [35]

    Wang, T. and R. J. Samworth (2018). High dimensional change point estimation via sparse projection.Journal of the Royal Statistical Society: Series B 80(1), 57–83

    2018

  36. [36]

    Wang, Y., C. Zou, Z. Wang, and G. Yin (2019). Multiple change-points detection in high dimension.Random Matrices: Theory and Applications 8(4), 1950014

    2019

  37. [37]

    Wu, W. B. (2005). Nonlinear system theory: Another look at dependence.Proceedings of the National Academy of Sciences of the United States of America 102(40), 14150–14154

    2005

  38. [38]

    Wu, W. B. and Y. N. Wu (2016). Performance bounds for parameter estimates of high-dimensional linear models with correlated errors.Electronic Journal of Statistics 10(1), 352–379

    2016

  39. [39]

    Yu, M. and X. Chen (2021). Finite sample change point inference and identification for high-dimensional mean vectors.Journal of the Royal Statistical Society: Series B 83(2), 247–270

    2021

  40. [40]

    Wang, and X

    Zhang, Y., R. Wang, and X. Shao (2022). Adaptive inference for change points in high-dimensional data.Journal of the American Statistical Association 117(540), 1751–1762. 106

    2022