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Extrapolation of extreme covariates in generalized additive regression using extreme-value theory

T0 review · 3 major / 0 minor · reviewed 2026-07-13 · grok-4.5

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Pith's one-line read GAMs predict better beyond the training range when their tails are forced linear on extreme-value scales.

desk verdict Solid, usable recipe that maps classical EVT limits onto GAMs for covariate extrapolation; the finite-threshold linearity assumption is real but not fatal for the intended moderate-extrapolation use case. read the letter →

arxiv 2607.08921 v1 pith:QYIHCAP6 submitted 2026-07-09 stat.ME

Viviana Carcaiso , Sebastian Engelke , Juliette Legrand , Thomas Opitz This is my paper
classification stat.ME MSC 62G3262J1262P12
keywords covariateextrapolationgeneralizedadditivemodelsmultivariateextreme-valuetheorypredictivemodelingconditionalextremesHüsler–Reisswildfirerisk
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

Standard generalized additive models fit flexible curves in the middle of the data but become unreliable once any covariate leaves the range seen in training. The paper shows that this can be fixed by first mapping covariates and (when continuous) the response onto marginal scales supplied by multivariate extreme-value theory, then forcing the predictor to become exactly linear above a high threshold while keeping ordinary smooths below it. Matching link functions (probit, logit, cauchit, identity) and error distributions follow from the same asymptotic frameworks, so the model stays coherent for both binary latent-variable responses and continuous responses. Simulations and a European wildfire study confirm that the hybrid construction improves scores that emphasize extreme covariate values without sacrificing overall fit. The practical payoff is more trustworthy forecasts when future climate drivers push environmental covariates outside historical bounds.

What carries the argument

Thresholded basis construction (Eq. 8): a penalized cubic spline that is free only below a high threshold u* on an EVT marginal scale and is forced to be exactly linear (continuous first derivative) above that threshold, glued to a link function and error law taken from the chosen extreme-value framework.

What would settle it

Generate data whose conditional mean remains nonlinear far into the covariate tail (or whose residual tails contradict the assumed error law) and check whether the hybrid model’s weighted logarithmic score or CRPS on extreme test covariates is still better than a plain spline GAM; if not, the central claim fails.

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Extended reading notes

Core claim

Integrating ordinary GAM smooths for the bulk of the covariate distribution with asymptotic linear models drawn from multivariate extreme-value theory, after transforming to the appropriate marginal scale and using a matching link function, yields better predictive performance for both binary and continuous responses whenever covariates exceed the observed training range.

Load-bearing premise

Once covariates pass a finite threshold on the chosen extreme-value scale, the true relationship between response (or latent variable) and those covariates is exactly linear with additive noise of the assumed form.

Editorial extensions

If this is right

  • Climate-impact models that feed future extremes of temperature, vapor-pressure deficit or wind into GAMs can replace unconstrained spline extrapolation with the hybrid linear tail and obtain more stable probability or size forecasts.
  • Binary event models (wildfire escalation, threshold exceedances) gain a theoretically justified probit or cauchit link once covariates are mapped to Laplace or Cauchy margins.
  • Any software package that already builds GAMs can implement the method by simply restricting the support of the spline basis and adding a linear term above a user-chosen threshold.
  • Model selection can treat the transition threshold itself as a hyper-parameter and choose it by weighted scoring rules that emphasize extreme covariates.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same marginal-scale-plus-linear-tail idea should transfer almost unchanged to neural nets whose activations already become linear outside the training range (e.g., ReLU networks).
  • When several covariates can be extreme together, the risk-functional constructions of Sections 2.4–2.5 suggest a natural route to joint linear predictors that ordinary back-fitting cannot easily capture.
  • The coefficient of extreme point prediction introduced in the paper could serve as a diagnostic for any black-box model, not only GAMs, whenever one wants to know whether extreme predictions remain associated with extreme outcomes.
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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

3 major / 0 minor

Summary. The paper develops hybrid generalized additive models that retain flexible spline structure in the bulk of the covariate distribution and switch to linear (or location–scale linear) structure in the tails, with the linear form, marginal scale, link function and error family chosen to match classical multivariate extreme-value representations (Gaussian, conditional extremes / Heffernan–Tawn, Hüsler–Reiss, transformed-linear / regular variation). Binary responses are handled via a latent-variable construction; continuous responses via identity or location–scale links on the corresponding margins. Implementation uses modified spline bases that enforce linearity above a finite threshold u*, with performance assessed by (weighted) proper scores, AUC/AUPRC and AIC. Simulations with deliberately more extreme test covariates, and a leave-one-year-out European wildfire application (escalation probability and burnt area), report gains especially on scores restricted to extreme covariates.

Significance. Covariate extrapolation under distribution shift is a genuine and under-addressed problem for GAMs in climate and environmental applications. The paper’s main contribution is a systematic, theory-guided mapping from four standard EVT frameworks to concrete choices of marginal transform, link and response family that can be fitted with existing GAM software (mgcv). The coefficient of extreme point prediction, the weighted scoring construction that targets extreme covariates rather than extreme responses, and the explicit treatment of both binary (latent) and continuous cases are useful. Simulations and leave-one-year CV on real wildfire data give reproducible empirical support for modest but consistent gains when the hybrid structure is used. If the finite-threshold linearity assumption is approximately valid, the method is a practical and interpretable tool for moderate extrapolation.

major comments (3)
  1. §5.1–5.2: All simulation scenarios generate data from the same hybrid class that is later fitted (nonlinear spline bulk + exact linear tail + error family matching the link). Tables 2–3 therefore measure recovery under correct specification, not robustness of the forced linear extrapolation. Because the central claim is improved prediction under covariate extrapolation in general, at least one misspecification design is needed (e.g., nonlinear tail on the EVT scale, wrong error tails, or asymptotic independence when an AD model is fitted) so that bias of the linear constraint can be quantified.
  2. §2.3–2.5 and Eq. (8): The EVT limits supply asymptotic linearity (or multiplicative structure that becomes additive after log), not exact linearity above a finite u*. The paper treats u* as a free hyperparameter and never reports residual diagnostics, estimated second derivatives, or sensitivity of weighted scores to u* (or to γ in the CE models). In §6 the wildfire gains on weighted scores are small (e.g., LogS_w 0.190→0.185; 1-AUC_w 0.298→0.284). Without evidence that the second derivative of the partial effect is near zero above the chosen thresholds, it is unclear whether the reported gains come from the EVT-motivated structure or from reduced boundary variance of a simpler tail.
  3. Eq. (3) (multivariate conditional extremes): The product form ∏(X_j^(L))^γ_j for the residual scale is proposed without a derivation from a joint limiting measure, and the necessary constraints on the γ_j (already tightened for the univariate case via Arendarczyk–Dębicki) are not restated for the product. Either a short justification under a joint CE or r-Pareto construction, or a clear statement that Eq. (3) is a pragmatic working model, is required before the multivariate CE results can be treated as theory-backed.

Circularity Check

0 steps flagged · score 1.0 of 10

No load-bearing circularity: linear tail forms are classical EVT limits, not redefined from the paper's own fits; evaluation is out-of-sample.

full rationale

The paper's derivation chain starts from four pre-existing multivariate extremes frameworks (multivariate Gaussian, Heffernan–Tawn conditional extremes 2004, multivariate regular variation / r-Pareto, Hüsler–Reiss 1989, transformed-linear of Cooley–Thibaud / Lee–Cooley). On the corresponding marginal scales it obtains asymptotic linear (or log-linear) conditional structure for the response or latent variable, then matches link functions and error families (probit/logit/cauchit, identity/log, normal/Laplace/Student-t). These structures are then imposed inside a GAM via a modified spline basis that is exactly linear above a finite threshold u* (Eqs. 6–8). The finite-threshold linearity is an explicit modeling assumption, not a quantity derived from or fitted to the same observations that are later scored. Simulations generate data from exactly the hybrid (bulk spline + linear tail + matching error) and evaluate proper scores / AUC / AUPRC on a deliberately extreme-enriched held-out set; the wildfire analysis uses leave-one-year-out cross-validation. Performance gains are therefore not forced by construction. Self-citations (Buriticá–Engelke progression, Legrand et al. 2025, Dombry–Legrand–Opitz, Opitz 2016, Bolin–Engelke et al.) supply related methodology or spatial analogues but are not invoked as uniqueness theorems that forbid alternatives or that redefine the classical limits in terms of the present paper's parameters. No step reduces a claimed prediction or first-principles result to its own fitted inputs. Score 1 reflects only the presence of non-load-bearing co-author citations.

Assumptions & free parameters 4 free parameters · 4 assumptions · 2 invented entities

The central claim rests on classical EVT limit theorems (treated as domain assumptions), the modeling choice that the conditional mean becomes exactly linear above a finite threshold, and a handful of free hyperparameters (thresholds, γ values, spline penalties). No new physical entities are postulated; the only invented objects are the hybrid estimator and the coefficient of extreme point prediction.

free parameters (4)
  • linearity threshold u* (per covariate)
    Chosen as a high empirical quantile; controls where the spline ends and the linear tail begins. Not estimated jointly with the coefficients.
  • conditional-extremes exponent γ
    Fixed at discrete values 0, 1/4, 1/2 in simulations and application; constrained by error-tail arguments but not estimated from data.
  • GPD thresholds for marginal transforms
    Lower and upper quantiles used to fit the semi-parametric marginal distribution; affect the transformed scale on which linearity is imposed.
  • spline roughness penalty / basis dimension
    Standard mgcv smoothing parameters; influence how much curvature is allowed below the linearity threshold.
assumptions (4)
  • domain assumption Multivariate regular variation / conditional extremes / Hüsler–Reiss / transformed-linear limits hold for the joint distribution of (Y,X) after suitable marginal transforms.
    Invoked throughout Section 2 to justify the linear tail structures; taken from the classical EVT literature.
  • ad hoc to paper Above a finite threshold the conditional expectation (or latent mean) is exactly linear in the transformed covariates with additive error of the assumed family.
    The practical modeling assumption that turns the asymptotic statements into a finite-sample GAM (Eqs. 6–8).
  • domain assumption Binary responses arise from a continuous latent variable exceeding a fixed threshold.
    Standard latent-variable construction used in Section 4.1 to transfer continuous EVT models to binary data.
  • standard math Product of independent Weibull-type random variables remains Weibull-type, yielding necessary constraints on γ.
    Cited from Arendarczyk & Dębicki (2011) and used to restrict γ for normal/Laplace/exponential errors.
invented entities (2)
  • coefficient of extreme point prediction χ(Y, Ŷ(X))
    purpose: Quantifies asymptotic dependence between the response and the model's point predictor under covariate extremes.
    Defined in Eq. (2); a natural but paper-specific adaptation of the classical χ coefficient to the predictive setting.
  • hybrid GAM with forced linear tail after threshold u*
    purpose: Practical estimator that glues a penalized spline bulk to an EVT-motivated linear tail.
    The main methodological object of the paper (Eqs. 6–8); no independent existence outside this construction.

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Cite this review

Pith. "Pith review of Extrapolation of extreme covariates in generalized additive regression using extreme-value theory." pith.science (2026). https://pith.science/paper/QYIHCAP6

@misc{pith2026260708921,
  author       = {Pith},
  title        = {Pith review of: Extrapolation of extreme covariates in generalized additive regression using extreme-value theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QYIHCAP6}},
  note         = {Machine review of arXiv:2607.08921}
}
read the original abstract

We propose methods to enhance the predictive performance of generalized additive models (GAMs) in the context of covariate extrapolation, where predictions rely on covariates beyond their observed range. When using predictive models such as GAMs, shifts in the covariate distribution between training and prediction datasets can occur. Ignoring this issue may lead to inaccurate predictions in the tail of the covariate distributions. For example, this problem is particularly critical in climate-change scenarios, where covariates simulated from future climate scenarios are likely to contain more extreme conditions. Our approach integrates GAMs for the bulk of covariate distributions with asymptotic models from multivariate extreme-value theory at high covariate values. We consider binary responses based on a latent variable assumption, and also continuous responses. For large values of the covariates, on a specific marginal scale motivated by extreme-value theory the latent variable or continuous response is assumed to depend linearly on the covariates with an additive error term, when using an appropriate link function. In an application to wildfires in Europe, we explore how the new method can improve predictions, using environmental and meteorological covariates.

Figures

Figures reproduced from arXiv: 2607.08921 by the authors.

Figure 1
Figure 1. Examples illustrating the effect of covariate and response scaling on model fit under different covariate distributions and error terms. Within each row, the data are identical across columns, but the covariate scale changes (uniform on (0, 1), Pareto, and standard exponential from left to right). In the third column, both covariate and response are shown on standard exponential margins; see Appendix A. Model estima… view at source ↗
Figure 2
Figure 2. Examples of simulated data under different scenarios. Left: simulated covariate versus latent variable, with the true conditional mean (dashed) and the threshold defining the binary response (dotted). Right: simulated covariate versus binary response, with the true Pr(Y = 1 | X) (dashed). Different shades and symbols distinguish training and test observations. observations are divided into training set and test set … view at source ↗
Figure 3
Figure 3. Example of fitted binary regression models under different frameworks. Left: true and estimated covariate effects evaluated on the test set. Right: predicted versus true conditional probabilities Pr(Y = 1 | X) for the test set. Dotted vertical lines mark the threshold where linearity is imposed for each model. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Different fitted models in the continuous-response simulation. Conditional mean and 95% prediction interval on the test set are compared with the true data-generating function. The dotted vertical line marks the threshold where linearity is imposed. Left: standard Gaus…
Figure 5
Figure 5. Figure 5: Estimated covariate effects (on standard Laplace margins) on the probability of escalation to a large wildfire across years. Models use either a spline or a spline below a high threshold and a conditional extreme model (linear or constant) above it. The dotted vertical…
Figure 6
Figure 6. Figure 6: Effect of each covariate under different models on the expected fire size (on the log10 scale), conditional on all other covariates being fixed at their median. Shaded areas represent 95% confidence intervals, and the point cloud shows the relationship between each cov…
Figure 7
Figure 7. Figure 7: Comparison between standard Laplace and Laplace-alternative distribution. Left: probability density func￾tions. Right: logarithm of the probability density functions. and the quantile function is Q(p) =    log(4p) − 1 p < 0.25, 4p − 2 p ∈ [0.25, 0.75], 1 − log…

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Works this paper leans on

67 extracted references · 3 linked inside Pith

  1. [1]

    Electronic Journal of Statistics , volume=

    On regression in extreme regions , author=. Electronic Journal of Statistics , volume=. 2025 , publisher=

    2025

  2. [2]

    Extremes , volume=

    Regression-type analysis for multivariate extreme values , author=. Extremes , volume=. 2022 , publisher=

    2022

  3. [3]

    Proceedings of 3rd international conference on document analysis and recognition , volume=

    Random decision forests , author=. Proceedings of 3rd international conference on document analysis and recognition , volume=. 1995 , organization=

    1995

  4. [4]

    Machine learning , volume=

    Random forests , author=. Machine learning , volume=. 2001 , publisher=

    2001

  5. [5]

    The Journal of Machine Learning Research , volume=

    Analysis of a random forests model , author=. The Journal of Machine Learning Research , volume=. 2012 , publisher=

    2012

  6. [6]

    Regression: Models, methods and applications , pages=

    Regression models , author=. Regression: Models, methods and applications , pages=. 2022 , publisher=

    2022

  7. [7]

    Journal of the American Statistical Association , volume=

    Evaluation of binary classifiers for asymptotically dependent and independent extremes , author=. Journal of the American Statistical Association , volume=. 2025 , publisher=

    2025

  8. [8]

    Water Resources Research , volume=

    Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection , author=. Water Resources Research , volume=. 2016 , publisher=

    2016

Show all 67 references
  1. [9]

    1984 , publisher =

    Classification and Regression Trees , author =. 1984 , publisher =

    1984

  2. [10]

    Environmental Data Science , volume=

    Modeling of spatial extremes in environmental data science: Time to move away from max-stable processes , author=. Environmental Data Science , volume=. 2025 , publisher=

    2025

  3. [11]

    Journal of the American statistical Association , volume=

    Strictly proper scoring rules, prediction, and estimation , author=. Journal of the American statistical Association , volume=. 2007 , publisher=

    2007

  4. [12]

    R package version 0.4-2 , volume=

    Xgboost: extreme gradient boosting , author=. R package version 0.4-2 , volume=

  5. [13]

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

    A conditional approach for multivariate extreme values (with discussion) , author=. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=. 2004 , publisher=

    2004

  6. [14]

    2017 , publisher=

    Generalized additive models: an introduction with R , author=. 2017 , publisher=

    2017

  7. [15]

    , author=

    Development and structure of the Canadian forest fire weather index system. , author=

  8. [16]

    2011 , journal=

    Asymptotics of supremum distribution of a Gaussian process over a Weibullian time , author=. 2011 , journal=

    2011

  9. [17]

    Statistics , volume=

    Tail asymptotic of Weibull-type risks , author=. Statistics , volume=. 2014 , publisher=

    2014

  10. [18]

    Biometrika , volume=

    Decompositions of dependence for high-dimensional extremes , author=. Biometrika , volume=. 2019 , publisher=

    2019

  11. [19]

    arXiv preprint arXiv:2111.03754 , year=

    Transformed-linear prediction for extremes , author=. arXiv preprint arXiv:2111.03754 , year=

  12. [20]

    arXiv preprint arXiv:2210.12618 , year=

    Estimating probabilities of multivariate failure sets based on pairwise tail dependence coefficients , author=. arXiv preprint arXiv:2210.12618 , year=

    arXiv

  13. [21]

    Statistics & Probability Letters , volume=

    Maxima of normal random vectors: between independence and complete dependence , author=. Statistics & Probability Letters , volume=. 1989 , publisher=

    1989

  14. [22]

    arXiv preprint arXiv:2410.23246 , year=

    Progression: an extrapolation principle for regression , author=. arXiv preprint arXiv:2410.23246 , year=

    arXiv

  15. [23]

    Extremes , pages=

    Weak signals and heavy tails: learning theory meets extreme value analysis , author=. Extremes , pages=. 2026 , publisher=

    2026

  16. [24]

    R package version , volume=

    Package ‘mgcv’ , author=. R package version , volume=

  17. [25]

    Journal of Multivariate Analysis , volume=

    Dense classes of multivariate extreme value distributions , author=. Journal of Multivariate Analysis , volume=. 2013 , publisher=

    2013

  18. [26]

    Advances in Neural Information Processing Systems , volume=

    On binary classification in extreme regions , author=. Advances in Neural Information Processing Systems , volume=

  19. [27]

    Stat , volume=

    Sub-asymptotic motivation for new conditional multivariate extreme models , author=. Stat , volume=. 2021 , publisher=

    2021

  20. [28]

    2006 , publisher=

    Extreme value theory: an introduction , author=. 2006 , publisher=

    2006

  21. [29]

    2008 , publisher=

    Extreme values, regular variation, and point processes , author=. 2008 , publisher=

    2008

  22. [30]

    Journal of the Royal Statistical Society: Series C (Applied Statistics) , volume=

    The multivariate Gaussian tail model: An application to oceanographic data , author=. Journal of the Royal Statistical Society: Series C (Applied Statistics) , volume=. 2000 , publisher=

    2000

  23. [31]

    Journal of the American Statistical Association , volume=

    Generalized additive models: some applications , author=. Journal of the American Statistical Association , volume=. 1987 , publisher=

    1987

  24. [32]

    Statistics and its Interface , volume=

    Functional regular variations, Pareto processes and peaks over threshold , author=. Statistics and its Interface , volume=. 2015 , publisher=

    2015

  25. [33]

    Estimation of h

    Engelke, Sebastian and Malinowski, Alexander and Kabluchko, Zakhar and Schlather, Martin , journal=. Estimation of h. 2015 , publisher=

    2015

  26. [34]

    Pareto Processes for Threshold Exceedances in Spatial Extremes , year =

    Dombry, Cl. Pareto Processes for Threshold Exceedances in Spatial Extremes , year =. Handbook on Statistics of Extremes , publisher =

  27. [35]

    Extremes , volume=

    Dependence measures for extreme value analyses , author=. Extremes , volume=. 1999 , publisher=

    1999

  28. [36]

    2009 , journal =

    The extremogram: A correlogram for extreme events , author=. 2009 , journal =

    2009

  29. [37]

    Annals of the Institute of Statistical Mathematics , volume=

    Bivariate extreme statistics , author=. Annals of the Institute of Statistical Mathematics , volume=. 1960 , publisher=

    1960

  30. [38]

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

    Engression: extrapolation through the lens of distributional regression , author=. Journal of the Royal Statistical Society Series B: Statistical Methodology , pages=. 2024 , publisher=

    2024

  31. [39]

    A review of spline function procedures in

    Perperoglou, Aris and Sauerbrei, Willi and Abrahamowicz, Michal and Schmid, Matthias , journal=. A review of spline function procedures in. 2019 , publisher=

    2019

  32. [40]

    Journal of the American Statistical Association , volume=

    Smoothing parameter and model selection for general smooth models , author=. Journal of the American Statistical Association , volume=. 2016 , publisher=

    2016

  33. [41]

    2009 , publisher=

    The Elements of Statistical Learning , author=. 2009 , publisher=

    2009

  34. [42]

    1990 , publisher=

    Spline Models for Observational Data , author=. 1990 , publisher=

    1990

  35. [43]

    1994 , publisher=

    Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach , author=. 1994 , publisher=

    1994

  36. [44]

    Eilers, Paul H. C. and Marx, Brian D. , journal=. Flexible smoothing with

  37. [45]

    Journal of the Royal Statistical Society: Series B (Statistical Methodology) , volume=

    Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations , author=. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , volume=. 2009 , publisher=

    2009

  38. [46]

    Statistical Science , pages=

    Forecaster's dilemma: Extreme events and forecast evaluation , author=. Statistical Science , pages=. 2017 , publisher=

    2017

  39. [47]

    Management Science , volume=

    Scoring rules for continuous probability distributions , author=. Management Science , volume=. 1976 , publisher=

    1976

  40. [48]

    Journal of the Royal Statistical Society: Series B (Methodological) , volume=

    Rational decisions , author=. Journal of the Royal Statistical Society: Series B (Methodological) , volume=. 1952 , publisher=

    1952

  41. [49]

    Monthly weather review , volume=

    Verification of forecasts expressed in terms of probability , author=. Monthly weather review , volume=

  42. [50]

    Biodiversity Informatics , year =

    Presence-only and presence-absence data for comparing species distribution modeling methods , author =. Biodiversity Informatics , year =

  43. [51]

    Journal of the Royal Statistical Society Series C: Applied Statistics , volume=

    Generalized additive models for location, scale and shape , author=. Journal of the Royal Statistical Society Series C: Applied Statistics , volume=. 2005 , publisher=

    2005

  44. [52]

    Constructive theory of functions of several variables: proceedings of a conference held at oberwolfach April 25--May 1, 1976 , pages=

    Splines minimizing rotation-invariant semi-norms in Sobolev spaces , author=. Constructive theory of functions of several variables: proceedings of a conference held at oberwolfach April 25--May 1, 1976 , pages=. 2006 , organization=

    1976

  45. [53]

    Journal of Business & Economic Statistics , volume=

    Comparing density forecasts using threshold-and quantile-weighted scoring rules , author=. Journal of Business & Economic Statistics , volume=. 2011 , publisher=

    2011

  46. [54]

    2025 , MONTH = Apr, DOI =

    Ruffault, Julien and Pimont, Fran. 2025 , MONTH = Apr, DOI =

    2025

  47. [55]

    PloS one , volume=

    The precision-recall plot is more informative than the ROC plot when evaluating binary classifiers on imbalanced datasets , author=. PloS one , volume=. 2015 , publisher=

    2015

  48. [56]

    Pattern recognition letters , volume=

    An introduction to ROC analysis , author=. Pattern recognition letters , volume=. 2006 , publisher=

    2006

  49. [57]

    Biometrika , volume=

    Statistics for near independence in multivariate extreme values , author=. Biometrika , volume=. 1996 , publisher=

    1996

  50. [58]

    The annals of applied statistics , volume=

    Spatiotemporal wildfire modeling through point processes with moderate and extreme marks , author=. The annals of applied statistics , volume=. 2023 , publisher=

    2023

  51. [59]

    Journal of Computational and Graphical Statistics , volume=

    Local linear forests , author=. Journal of Computational and Graphical Statistics , volume=. 2020 , publisher=

    2020

  52. [60]

    arXiv preprint arXiv:1803.08375 , year=

    Deep learning using rectified linear units (relu) , author=. arXiv preprint arXiv:1803.08375 , year=

    arXiv

  53. [61]

    arXiv preprint arXiv:2512.23395 , year=

    Intrinsic Whittle--Mat 'ern fields and sparse spatial extremes , author=. arXiv preprint arXiv:2512.23395 , year=

  54. [62]

    , title =

    Anderson, Theodore W. , title =

  55. [63]

    Statistical inference for H

    Hentschel, Manuel and Engelke, Sebastian and Segers, Johan , journal=. Statistical inference for H. 2025 , publisher=

    2025

  56. [64]

    IEEE Signal Processing Letters , volume=

    On the multivariate Laplace distribution , author=. IEEE Signal Processing Letters , volume=. 2006 , publisher=

    2006

  57. [65]

    Advances in Applied Probability , volume=

    Linking representations for multivariate extremes via a limit set , author=. Advances in Applied Probability , volume=. 2022 , publisher=

    2022

  58. [66]

    arXiv preprint arXiv:2509.22501 , year=

    Modelling non-stationary extremal dependence through a geometric approach , author=. arXiv preprint arXiv:2509.22501 , year=

  59. [67]

    Spatial Statistics , volume=

    Modeling asymptotically independent spatial extremes based on Laplace random fields , author=. Spatial Statistics , volume=. 2016 , publisher=

    2016

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