Pith. sign in

REVIEW 2 major objections 2 minor 84 references

Out-of-Distribution generalization of quantile regression with heavy tailed inputs: an SVM approach

T0 review · 2 major / 2 minor · reviewed 2026-06-28 · grok-4.3

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

Pith's one-line read A reproducing kernel Hilbert space support vector machine framework enables extrapolation in quantile regression for heavy-tailed covariates with finite-sample guarantees.

desk verdict SVM for extreme quantile regression offers a clean unification but finite-sample bounds may not account for stochastic tail sample sizes. read the letter →

arxiv 2606.00265 v1 pith:7WGBKDVK submitted 2026-05-29 stat.ML cs.LG

Baptiste Leroux , Clément Dombry , Anne Sabourin This is my paper · ORCID
classification stat.MLcs.LG
keywords quantileregressionextremevaluetheorysupportvectormachinesreproducingkernelHilbertspacesout-of-distributiongeneralizationheavytaileddistributionsmultivariateextremesfinitesampleguarantees
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

The paper develops a method for performing quantile regression when covariates take values much larger than those seen in training, which matters for forecasting rare but impactful events. It assumes the covariate distribution is regularly varying so that extremes are determined by their direction from the origin. The approach formulates this as minimizing an asymptotic conditional risk in a reproducing kernel Hilbert space, leading to an SVM estimator with finite-sample guarantees. This combines ideas from machine learning and extreme value theory without needing to transform the responses. The method is illustrated on real river flow data.

What carries the argument

The asymptotic conditional risk localized to the tail of the covariate distribution via angular components, minimized in a reproducing kernel Hilbert space to produce the SVM estimator.

What would settle it

Generating synthetic data from a distribution with heavy tails but without regular variation and checking whether the estimator still achieves low extrapolation error.

Watch

Extended reading notes

Core claim

The authors claim that minimizing an asymptotic conditional risk that localizes learning to the angular components of extreme covariate observations, when performed over a reproducing kernel Hilbert space, yields a support vector machine estimator for extreme quantiles that generalizes to out-of-distribution inputs with finite-sample learning guarantees under mild regularity assumptions.

Load-bearing premise

The covariate distribution is regularly varying, so extreme observations can be characterized through their angular components.

Editorial extensions

If this is right

  • The framework handles high-dimensional and nonlinear settings for quantile extrapolation.
  • It works with unbounded response variables without restrictive transformations.
  • Finite-sample learning guarantees hold under mild regularity assumptions.
  • The approach unifies statistical learning theory with multivariate extreme value theory.

Reading between the lines

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

  • This localization to angles could be applied to other regression tasks involving tail behavior, such as conditional expected shortfall.
  • The method's flexibility with kernels might allow better adaptation to different dependence structures in extremes compared to linear models.
  • In applications like climate modeling, it could provide more reliable predictions for unprecedented covariate values.
Share X Bluesky LinkedIn Reddit HN

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

2 major / 2 minor

Summary. The paper proposes an SVM framework in RKHS for extreme quantile regression under regular variation of covariates, localizing learning via minimization of an asymptotic conditional risk on angular components of extremes. It claims finite-sample learning guarantees under mild regularity assumptions, accommodates unbounded responses without transformations, and demonstrates the approach on Danube river flow data.

Significance. A valid finite-sample theory for tail extrapolation in quantile regression would usefully connect statistical learning theory with multivariate extremes, offering a tractable alternative to purely asymptotic EVT methods when the number of tail observations is limited.

major comments (2)
  1. [Abstract / finite-sample guarantees section] Abstract and the section stating the finite-sample guarantees: the claim of finite-sample bounds under 'mild regularity assumptions' is load-bearing, yet regular variation alone makes the number of exceedances over any high threshold a random variable whose lower tail is uncontrolled (no second-order regular variation or moment conditions on the angular measure are stated). This leaves open the possibility that the effective sample for the localized empirical risk minimizer is empty or near-empty with non-negligible probability, rendering the transferred SVM generalization bounds vacuous for any fixed n.
  2. [Method / theoretical construction] The construction that minimizes the asymptotic conditional risk localized to angular components (prior to applying RKHS SVM bounds): the localization step invokes regular variation to justify focusing on angles, but the subsequent finite-sample transfer does not appear to condition on or lower-bound the realized number of tail points, so the 'mild assumptions' do not guarantee that the empirical risk is well-defined or that the derived rates apply uniformly.
minor comments (2)
  1. [Experiments] The empirical section on Danube data would benefit from explicit reporting of the number of exceedances used in each experiment and sensitivity checks to threshold choice.
  2. [Preliminaries] Notation for the angular measure and the precise definition of the localized risk should be cross-referenced to the regular-variation assumptions for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and insightful comments regarding the finite-sample guarantees. We respond to each major comment below and indicate where revisions will be made to clarify the role of the random number of exceedances.

read point-by-point responses

  1. Referee: [Abstract / finite-sample guarantees section] Abstract and the section stating the finite-sample guarantees: the claim of finite-sample bounds under 'mild regularity assumptions' is load-bearing, yet regular variation alone makes the number of exceedances over any high threshold a random variable whose lower tail is uncontrolled (no second-order regular variation or moment conditions on the angular measure are stated). This leaves open the possibility that the effective sample for the localized empirical risk minimizer is empty or near-empty with non-negligible probability, rendering the transferred SVM generalization bounds vacuous for any fixed n.

    Authors: We agree that regular variation alone leaves the lower tail of the exceedance count uncontrolled, and that the original presentation did not explicitly condition the finite-sample SVM bounds on a positive number of tail observations. The localization argument relies on the angular measure, but the transfer of generalization bounds from the RKHS SVM to the empirical angular sample requires the realized sample size to be positive. We will revise the abstract and the guarantees section to state that all finite-sample bounds are conditional on the event that at least k exceedances are observed (for a user-chosen k), and we will add a short discussion of the probability of this event under the maintained regular-variation assumption. revision: yes

  2. Referee: [Method / theoretical construction] The construction that minimizes the asymptotic conditional risk localized to angular components (prior to applying RKHS SVM bounds): the localization step invokes regular variation to justify focusing on angles, but the subsequent finite-sample transfer does not appear to condition on or lower-bound the realized number of tail points, so the 'mild assumptions' do not guarantee that the empirical risk is well-defined or that the derived rates apply uniformly.

    Authors: The referee correctly identifies that the finite-sample transfer step does not currently condition on the realized number of angular points. The asymptotic conditional risk is well-defined via regular variation, yet the empirical risk minimizer is only defined when at least one tail point is observed. We will revise the theoretical construction section to make the conditioning explicit: all rates will be stated conditionally on the number of observed exceedances N_n(u) ≥ 1, and we will note that the unconditional guarantee then follows by multiplying by P(N_n(u) ≥ 1). This change does not alter the core SVM analysis but renders the statements uniform over the random sample size. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation builds on external regular variation and SVM theory.

full rationale

The abstract and description present a novel SVM framework for extreme quantile regression that minimizes an asymptotic conditional risk localized via regular variation, then transfers finite-sample RKHS bounds. No equations or steps are shown that reduce a claimed prediction or guarantee to a fitted input or self-citation by construction. The approach unifies existing ideas from statistical learning and extremes without self-definitional loops, fitted-input predictions, or load-bearing self-citations that collapse the central claim. This is the expected honest non-finding for a paper whose core construction remains independent of its own outputs.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The central claim rests on regular variation assumptions from extreme value theory to enable angular characterization of tails.

assumptions (1)
  • domain assumption Regular variation assumptions on the covariate distribution
    Allows extreme observations to be characterized through angular components and localizes learning in the tail.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Out-of-Distribution generalization of quantile regression with heavy tailed inputs: an SVM approach." pith.science (2026). https://pith.science/paper/7WGBKDVK

@misc{pith2026260600265,
  author       = {Pith},
  title        = {Pith review of: Out-of-Distribution generalization of quantile regression with heavy tailed inputs: an SVM approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7WGBKDVK}},
  note         = {Machine review of arXiv:2606.00265}
}
read the original abstract

We study quantile regression in an extrapolation regime where the covariate takes unusually large values. Under regular variation assumptions, extreme observations can be effectively characterized through their angular components, enabling learning strategies that focus on the angle of the most extreme observations. This approach is formalized through the minimization of an asymptotic conditional risk that localizes learning in the tail of the covariate distribution. We propose a novel Support Vector Machine (SVM) framework for extreme quantile regression, leveraging reproducing kernel Hilbert spaces to handle high-dimensional and nonlinear settings. Our method also accommodates unbounded response variables and avoids restrictive transformations. We establish finite-sample learning guarantees under mild regularity assumptions. The proposed framework unifies ideas from statistical learning and multivariate extremes, providing a tractable and theoretically grounded approach to extrapolation. We complement our theoretical findings with an empirical study on river flow data from the Danube, demonstrating the practical relevance of our methods.

Figures

Figures reproduced from arXiv: 2606.00265 by the authors.

Figure 1
Figure 1. The geographical distribution of the gauging stations along the Danube in Bavaria, Germany. [PITH_FULL_IMAGE:figures/full_fig_p018_1.png] view at source ↗
Figure 2
Figure 2. Left panel: log-log Scatter plot of Z with respect to ∥X∥ for station 18, on the 5% most extreme observations. Right panel: Scatter plot of Y = Z/∥X∥ with respect to ∥X∥ for station 18, on the 5% most extreme observations. Points are colored red if the maximum for the norm ∥X∥∞ is attained in one of the three stations 16, 17 or 18, and blue otherwise. 0.0 0.1 0.2 0.3 0.4 0.015 0.016 0.017 0.018 0.019 SVM ERM [PITH_… view at source ↗
Figure 3
Figure 3. Mean approximated asymptotic pinball risk over 10 permutations of the whole dataset with [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Left panel: Prediction versus true values for the prediction of [PITH_FULL_IMAGE:figures/full_fig_p021_4.png]
Figure 5
Figure 5. Figure 5: Predictions against true values for different approaches, in the original scale of the dataset, [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

84 extracted references · 10 canonical work pages

  1. [1]

    The Annals of Statistics , pages=

    Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution , author=. The Annals of Statistics , pages=. 2009 , publisher=

    2009

  2. [2]

    2026 , eprint =

    Extrapolation in Statistical Learning with Extreme Value Theory , author =. 2026 , eprint =

    2026

  3. [3]

    Econometrica , volume =

    Koenker, Roger and Bassett, Gilbert , title =. Econometrica , volume =. 1978 , publisher =

    1978

  4. [4]

    Annual Review of Economics , volume =

    Koenker, Roger , title =. Annual Review of Economics , volume =. 2020 , doi =

    2020

  5. [5]

    2012 , publisher=

    Approximate distributions of order statistics: with applications to nonparametric statistics , author=. 2012 , publisher=

    2012

  6. [6]

    Tail index estimation, concentration and adaptivity , author=

  7. [7]

    Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach , author =

  8. [8]

    Insurance: Mathematics and Economics , volume =

    Center-outward quantiles and the measurement of multivariate risk , author =. Insurance: Mathematics and Economics , volume =. 2020 , publisher =

    2020

Show all 84 references
  1. [9]

    Computational Statistics & Data Analysis , volume =

    Exact computation of the halfspace depth , author =. Computational Statistics & Data Analysis , volume =. 2016 , publisher =

    2016

  2. [10]

    Conference on learning theory , pages =

    Learning the dependence structure of rare events: a non-asymptotic study , author =. Conference on learning theory , pages =. 2015 , organization =

    2015

  3. [11]

    Statistics & Probability Letters , volume =

    Uniform concentration bounds for frequencies of rare events , author =. Statistics & Probability Letters , volume =. 2022 , publisher =

    2022

  4. [12]

    2018 , publisher =

    Foundations of machine learning , author =. 2018 , publisher =

    2018

  5. [13]

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

    Estimation of extreme depth-based quantile regions , author =. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume =. 2017 , publisher =

    2017

  6. [14]

    Annals of Statistics , volume =

    Bridging centrality and extremity: Refining empirical data depth using extreme value statistics , author =. Annals of Statistics , volume =. 2015 , publisher =

    2015

  7. [15]

    2023 , bdsk-url-1 =

    St. 2023 , bdsk-url-1 =. doi:10.3150/22-BEJ1562 , journal =

    2023 doi

  8. [16]

    Nagy, Stanislav and Demni, Houyem and Buttarazzi, Davide and Porzio, Giovanni C. , doi =. Advances in Data Analysis and Classification , title =. 2023 , bdsk-url-1 =

    2023

  9. [17]

    Einmahl and Vladimir I

    John H.J. Einmahl and Vladimir I. Piterbarg and Laurens de Haan , doi =. The Annals of Statistics , keywords =. 2001 , bdsk-url-1 =

    2001

  10. [18]

    2024 , eprint =

    Theoretical properties of angular halfspace depth , author =. 2024 , eprint =

    2024

  11. [19]

    2023 , primaryclass =

    Exact computation of angular halfspace depth , author =. 2023 , primaryclass =

    2023

  12. [20]

    2020 , bdsk-url-1 =

    Anja Jan. 2020 , bdsk-url-1 =. doi:10.1214/20-EJS1689 , journal =

    2020 doi

  13. [21]

    2007 , publisher =

    Heavy-tail phenomena: probabilistic and statistical modeling , author =. 2007 , publisher =

    2007

  14. [22]

    2008 , publisher =

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

    2008

  15. [23]

    Extreme value theory: an introduction , year =

    De Haan, Laurens and Ferreira, Ana , publisher =. Extreme value theory: an introduction , year =

  16. [24]

    Electronic Journal of Statistics , volume=

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

    2025

  17. [25]

    Publications de l'Institut Math

    Regular variation for measures on metric spaces , author =. Publications de l'Institut Math

  18. [26]

    2006 , publisher =

    Statistics of extremes: theory and applications , author =. 2006 , publisher =

    2006

  19. [27]

    Zuo and R

    Y. Zuo and R. Serfling , year =. General notions of statistical depth function , journal =

  20. [28]

    doi:10.1051/ps/2016005 , journal =

    Nagy, Stanislav and Gijbels, Irène and Omelka, Marek and Hlubinka, Daniel , title =. doi:10.1051/ps/2016005 , journal =

    doi

  21. [29]

    and Serfling, R

    Zuo, Y. and Serfling, R. , journal =. Structural properties and convergence results for contours of sample statistical depth functions , volume =

  22. [30]

    Proceedings of the International Congress of Mathematicians, Vancouver, 1975 , volume =

    Mathematics and the picturing of data , author =. Proceedings of the International Congress of Mathematicians, Vancouver, 1975 , volume =. 1975 , publisher =

    1975

  23. [31]

    Small , journal =

    Christopher G. Small , journal =. Measures of Centrality for Multivariate and Directional Distributions , urldate =

  24. [32]

    Liu and Kesar Singh , doi =

    Regina Y. Liu and Kesar Singh , doi =. The Annals of Statistics , keywords =. 1992 , bdsk-url-1 =

    1992

  25. [33]

    Werner , doi =

    Florian Besau and Elisabeth M. Werner , doi =. The spherical convex floating body , url =. Advances in Mathematics , keywords =. 2016 , bdsk-url-1 =

    2016

  26. [34]

    2017 , issn =

    Uniform convergence rates for halfspace depth , journal =. 2017 , issn =. doi:https://doi.org/10.1016/j.spl.2017.01.002 , url =

    2017 doi

  27. [35]

    and Wellner, Jon A

    Shorack, Galen R. and Wellner, Jon A. , publisher =. Empirical Processes with Applications to Statistics , year =

  28. [36]

    2013 , publisher =

    A probabilistic theory of pattern recognition , author =. 2013 , publisher =

    2013

  29. [37]

    Principles of nonparametric learning , pages =

    Pattern classification and learning theory , author =. Principles of nonparametric learning , pages =. 2002 , publisher =

    2002

  30. [38]

    2002 , series =

    Real Analysis and Probability , author =. 2002 , series =

    2002

  31. [39]

    N. H. Bingham and C. M. Goldie and J. L. Teugels , publisher =. Regular variation , year =

  32. [40]

    2008 , publisher=

    Support vector machines , author=. 2008 , publisher=

    2008

  33. [41]

    Comptes Rendus Mathematique , volume=

    A Bennett concentration inequality and its application to suprema of empirical processes , author=. Comptes Rendus Mathematique , volume=. 2002 , publisher=

    2002

  34. [42]

    Journal of Complexity , volume=

    The covering number in learning theory , author=. Journal of Complexity , volume=. 2002 , publisher=

    2002

  35. [43]

    Journal of the Royal Statistical Society-Series A Statistics in Society , volume=

    Weak convergence and empirical processes with applications to statistics , author=. Journal of the Royal Statistical Society-Series A Statistics in Society , volume=. 1997 , publisher=

    1997

  36. [44]

    Bernoulli , volume=

    Estimating conditional quantiles with the help of the pinball loss , author=. Bernoulli , volume=

  37. [45]

    Annals of Statistics , volume=

    Statistical performance of support vector machines , author=. Annals of Statistics , volume=

  38. [46]

    Electronic Journal of Statistics , volume=

    Optimal regression rates for SVMs using Gaussian kernels , author=. Electronic Journal of Statistics , volume=

  39. [47]

    Journal d’Analyse Math

    A modulus of smoothness on the unit sphere , author=. Journal d’Analyse Math. 1999 , publisher=

    1999

  40. [48]

    Advances in Mathematics , volume=

    Moduli of smoothness and approximation on the unit sphere and the unit ball , author=. Advances in Mathematics , volume=. 2010 , publisher=

    2010

  41. [49]

    arXiv preprint arXiv:1702.06899 , year=

    liquidSVM: A fast and versatile SVM package , author=. arXiv preprint arXiv:1702.06899 , year=

    arXiv

  42. [50]

    Annales de l'IHP Probabilit

    On consistency of kernel density estimators for randomly censored data: rates holding uniformly over adaptive intervals , author=. Annales de l'IHP Probabilit

  43. [51]

    Transactions of the American mathematical society , volume=

    Theory of reproducing kernels , author=. Transactions of the American mathematical society , volume=

  44. [52]

    2013 , HAL_ID =

    Boucheron, St. 2013 , HAL_ID =

    2013

  45. [53]

    Advances in Neural Information Processing Systems , volume=

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

  46. [54]

    arXiv preprint arXiv:2410.23246 , year=

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

  47. [55]

    Estimation of extreme risk regions under multivariate regular variation , author=

  48. [56]

    Stochastic processes and their applications , volume=

    On regular variation of probability densities , author=. Stochastic processes and their applications , volume=. 1987 , publisher=

    1987

  49. [57]

    Annals of Statistics , volume=

    Local Rademacher complexities , author=. Annals of Statistics , volume=. 2005 , publisher=

    2005

  50. [58]

    2013 , publisher=

    Probability in Banach Spaces: isoperimetry and processes , author=. 2013 , publisher=

    2013

  51. [59]

    Concentration Inequalities for Sums and Martingales , pages=

    Concentration inequalities for martingales , author=. Concentration Inequalities for Sums and Martingales , pages=. 2015 , publisher=

    2015

  52. [60]

    The Annals of Applied Statistics , volume=

    Extremes on river networks , author=. The Annals of Applied Statistics , volume=. 2015 , publisher=

    2015

  53. [61]

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

    Graphical models for extremes , author=. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=. 2020 , publisher=

    2020

  54. [62]

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

    Modelling extreme multivariate events , author=. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=. 1991 , publisher=

    1991

  55. [63]

    Analysis and Applications , volume=

    Estimating the approximation error in learning theory , author=. Analysis and Applications , volume=. 2003 , publisher=

    2003

  56. [64]

    Journal of Machine Learning Research , volume=

    Optimal learning rates for localized SVMs , author=. Journal of Machine Learning Research , volume=

  57. [65]

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

    Statistical methods for multivariate extremes: an application to structural design , author=. Journal of the Royal Statistical Society: Series C (Applied Statistics) , volume=. 1994 , publisher=

    1994

  58. [66]

    Le and Timothy D

    Ichiro Takeuchi and Quoc V. Le and Timothy D. Sears and Alexander J. Smola , title =. Journal of Machine Learning Research , year =

  59. [67]

    2011 , publisher=

    Reproducing kernel Hilbert spaces in probability and statistics , author=. 2011 , publisher=

    2011

  60. [68]

    arXiv preprint arXiv:2009.11848 , year=

    How neural networks extrapolate: From feedforward to graph neural networks , author=. arXiv preprint arXiv:2009.11848 , year=

    2009

  61. [69]

    Artificial Intelligence for the Earth Systems , volume=

    Validating deep learning weather forecast models on recent High-Impact extreme events , author=. Artificial Intelligence for the Earth Systems , volume=. 2025 , publisher=

    2025

  62. [70]

    Advances in Neural Information Processing Systems , volume=

    Heavy-tailed representations, text polarity classification & data augmentation , author=. Advances in Neural Information Processing Systems , volume=

  63. [71]

    arXiv preprint arXiv:2505.00835 , year=

    Multi-site modelling and reconstruction of past extreme skew surges along the French Atlantic coast , author=. arXiv preprint arXiv:2505.00835 , year=

    arXiv

  64. [72]

    Extremes , volume=

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

    2022

  65. [73]

    Extremal

    Chernozhukov, Victor and. Extremal. Handbook of

  66. [74]

    Bernoulli , volume =

    On Kernel Smoothing for Extremal Quantile Regression , author =. Bernoulli , volume =. doi:10.3150/12-BEJ466 , urldate =

    doi

  67. [75]

    Foundations of Computational mathematics , volume=

    Optimal rates for the regularized least-squares algorithm , author=. Foundations of Computational mathematics , volume=. 2007 , publisher=

    2007

  68. [76]

    arXiv preprint arXiv:2601.06264 , year=

    Graph structure learning for stable processes , author=. arXiv preprint arXiv:2601.06264 , year=

  69. [77]

    Machine learning , volume=

    A theory of learning from different domains , author=. Machine learning , volume=. 2010 , publisher=

    2010

  70. [78]

    , author=

    Covariate shift adaptation by importance weighted cross validation. , author=. Journal of Machine Learning Research , volume=

  71. [79]

    Extremes , pages=

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

    2026

  72. [80]

    ESAIM: probability and statistics , volume=

    Theory of classification: A survey of some recent advances , author=. ESAIM: probability and statistics , volume=. 2005 , publisher=

    2005

  73. [81]

    Annals of Statistics , volume=

    General nonexact oracle inequalities for classes with a subexponential envelope , author=. Annals of Statistics , volume=

  74. [82]

    Journal of machine learning research , volume=

    Stability and generalization , author=. Journal of machine learning research , volume=

  75. [83]

    The Annals of Statistics , volume=

    Causal discovery in heavy-tailed models , author=. The Annals of Statistics , volume=. 2021 , publisher=

    2021

  76. [84]

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

    Causal mechanism of extreme river discharges in the upper Danube basin network , author=. Journal of the Royal Statistical Society Series C: Applied Statistics , volume=. 2020 , publisher=

    2020

Pith tools

Reviewed June 28, 2026 · model on record in the stance chip above.