Research

STUPFLER Gilles

Lecturer in Statistics Research interests
  • Extreme value analysis 
  • Semi- and non-parametric statistics
  • M-estimation 
  • Missing data frameworks 
  • Hidden Markov models
Bureau 255 Téléphone +33 (0)2 99 05 32 55 Email gilles.stupfler@ensai.fr Adresse ENSAI
Campus de Ker Lann
51 Rue Blaise Pascal
BP 37203
35172 BRUZ Cedex

My main area of research is extreme value analysis. Much of my recent work in this direction has focused on how to measure and estimate extreme risk, particularly in actuarial and financial contexts.

I am also interested in nonparametric statistics and especially regression methods, as well as in the extreme value analysis of missing data models. 

My full academic CV, containing information about my qualifications, work experience, past and present teaching activities and research, can be found here.

 

(Most recent first)

  1. Daouia, A., Girard, S., Stupfler, G. (2020). Tail expectile process and risk assessment, Bernoulli 26(1): 531-556. 
  2. Stupfler, G. (2019). On a relationship between randomly and non-randomly thresholded empirical average excesses for heavy tails, Extremes 22(4): 749-769.
  3. Daouia, A., Gijbels, I., Stupfler, G. (2019). Extremiles: A new perspective on asymmetric least squares, Journal of the American Statistical Association 114(527): 1366-1381.
  4. Falk, M., Stupfler, G. (2019). The min-characteristic function: characterizing distributions by their min-linear projections, Sankhya, to appear. 
  5. Gardes, L., Girard, S., Stupfler, G. (2019). Beyond tail median and conditional tail expectation: extreme risk estimation using tail Lp-optimisation, Scandinavian Journal of Statistics, to appear.
  6. Falk, M., Stupfler, G. (2019). On a class of norms generated by nonnegative integrable distributions, Dependence Modeling 7(1): 259-278.
  7. Stupfler, G. (2019). On the study of extremes with dependent random right-censoring, Extremes 22(1): 97-129.
  8. Church, O., Derclaye, E., Stupfler, G. (2019). An empirical analysis of the design case law of the EU Member States, International Review of Intellectual Property and Competition Law 50(6): 685-719.
  9. Gardes, L., Stupfler, G. (2019). An integrated functional Weissman estimator for conditional extreme quantiles, REVSTAT: Statistical Journal 17(1): 109-144.
  10. Daouia, A., Girard, S., Stupfler, G. (2019). Extreme M-quantiles as risk measures: From L1 to Lp optimization, Bernoulli 25(1): 264-309. A version of the supplementary material containing corrections to certain proofs and the statement of Lemma 1 (the main results of the paper remain valid) is available here. [With thanks to Antoine Usseglio-Carleve]
  11. El Methni, J., Stupfler, G. (2018). Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions, Econometrics and Statistics 6: 129-148.
  12. Daouia, A., Girard, S., Stupfler, G. (2018). Estimation of tail risk based on extreme expectiles, Journal of the Royal Statistical Society: Series B 80(2): 263-292.
  13. Stupfler, G., Yang, F. (2018). Analyzing and predicting CAT bond premiums: a Financial Loss premium principle and extreme value modeling, ASTIN Bulletin 48(1): 375-411.
  14. El Methni, J., Stupfler, G. (2017). Extreme versions of Wang risk measures and their estimation for heavy-tailed distributions, Statistica Sinica 27(2): 907-930.
  15. Girard, S., Stupfler, G. (2017). Intriguing properties of extreme geometric quantiles, REVSTAT: Statistical Journal 15(1): 107-139.
  16. Falk, M., Stupfler, G. (2017). An offspring of multivariate extreme value theory: the max-characteristic function, Journal of Multivariate Analysis 154: 85-95.
  17. Stupfler, G. (2016). On the weak convergence of the kernel density estimator in the uniform topology, Electronic Communications in Probability 21(17): 1-13.
  18. Stupfler, G. (2016). Estimating the conditional extreme-value index under random right-censoring, Journal of Multivariate Analysis 144: 1-24.
  19. Girard, S., Stupfler, G. (2015). Extreme geometric quantiles in a multivariate regular variation framework, Extremes 18(4): 629-663.
  20. Meintanis, S.G., Stupfler, G. (2015). Transformations to symmetry based on the probability weighted characteristic function, Kybernetika 51(4): 571-587.
  21. Goegebeur, Y., Guillou, A., Stupfler, G. (2015). Uniform asymptotic properties of a nonparametric regression estimator of conditional tails, Annales de l'Institut Henri Poincaré (B): Probability and Statistics 51(3): 1190-1213.
  22. Gardes, L., Stupfler, G. (2015). Estimating extreme quantiles under random truncation, TEST 24(2): 207-227. An erratum, also published in TEST, is available here.
  23. Guillou, A., Loisel, S., Stupfler, G. (2015). Estimating the parameters of a seasonal Markov-modulated Poisson process, Statistical Methodology 26: 103-123.
  24. Stupfler, G. (2014). On the weak convergence of kernel density estimators in Lp spaces, Journal of Nonparametric Statistics 26(4): 721-735.
  25. Gardes, L., Stupfler, G. (2014). Estimation of the conditional tail index using a smoothed local Hill estimator, Extremes 17(1): 45-75.
  26. Girard, S., Guillou, A., Stupfler, G. (2014). Uniform strong consistency of a frontier estimator using kernel regression on high order moments, ESAIM: Probability and Statistics 18: 642-666.
  27. Stupfler, G. (2013). A moment estimator for the conditional extreme-value index, Electronic Journal of Statistics 7: 2298-2343.
  28. Guillou, A., Loisel, S., Stupfler, G. (2013). Estimation of the parameters of a Markov-modulated loss process in insurance, Insurance: Mathematics and Economics 53(2): 388-404.
  29. Girard, S., Guillou, A., Stupfler, G. (2013). Frontier estimation with kernel regression on high order moments, Journal of Multivariate Analysis 116: 172-189.
  30. Girard, S., Guillou, A., Stupfler, G. (2012). Estimating an endpoint with high order moments in the Weibull domain of attraction, Statistics and Probability Letters 82(12): 2136-2144.
  31. Girard, S., Guillou, A., Stupfler, G. (2012). Estimating an endpoint with high-order moments, TEST 21(4): 697-729.

Project title: Tail risk estimation across time and space
PhD supervisors: Abdelaati Daouia (Toulouse School of Economics) and Gilles Stupfler (ENSAI & CREST)
Duration: 3 years
Place of work: Rennes and/or Toulouse
Starting date: September 2020

Project description: 

The current state of the art in tail risk assessment relies on the use of quantile regression as a main instrument of risk protection. However, quantiles only measure the frequency of tail events and not their magnitude. Furthermore, in many important applications such as, for instance, natural sciences where modeling extreme events across time and space is a minimal requirement, the temporal and spatial nature of extremes is often ignored or addressed under the assumption of a constant extreme value index or that the response Y given the covariates X (typically latitude, longitude and/or altitude) has exactly a Pareto distribution, which is unreasonable in practice.

The overall objective of this PhD project is to paint a comprehensive picture of regression extremes by considering instead Conditional Tail Moments and generalized Lp−quantiles, in a realistic framework that allows for the (geographical) differentiation of tail risk across time. We will do so by adapting and extending some very recent results on Conditional Tail Moment and Lp-quantile regression from the standard i.i.d. setting to the dependent time series framework. The main tool is the use of asymptotic connections between these alternative risk measures and conditional (pure) quantiles. We will work out the theory by extending powerful Gaussian approximations of the tail empirical quantile process to the regression setup. The last stage of the project will be to analyze the finite-sample performance of the built estimators, both on simulated and real rainfall and earthquake data.

Project title: Extreme expectiles for short- and light-tailed distributions
Supervisors: Gilles Stupfler (ENSAI & CREST) and Abdelaati Daouia (Toulouse School of Economics)
Starting date: February-March 2020

Project description: 

The notion of expectiles, developed by Newey and Powell (1987), defines a least squares analogue of quantiles. Like the class of quantiles, expectiles define a law-invariant class of quantities depending on an asymmetry level τ ∈ (0,1). Unlike quantiles however, they are determined by tail expectations rather than solely tail probabilities. For this reason and many other theoretical and practical merits, tail expectiles have recently received a lot of attention, especially in actuarial and financial risk management. From the perspective of extreme value theory, Daouia et al. (2018, 2020) have recently provided tail expectile estimators based on top order statistics and/or asymmetric least squares (ALS) estimates. This translates into considering the expectile level τ depending on the available sample size n and converging to 1 as n goes to infinity. Their work is restricted to the class of heavy-tailed random variables, which is a natural modelling framework for extreme financial and actuarial risk assessment.

The class of heavy-tailed distributions, or Fréchet domain of attraction, is one of the three natural families of distributions in extreme value modelling. The other two classes are those of short-tailed distributions (or Weibull domain of attraction) and light-tailed distributions (or Gumbel domain of attraction). The goal of this dissertation is to extend the theory for inference on extreme expectiles to these classes of short- and light-tailed distributions. This is crucially important, for instance, in econometrics to enhance cost, production, allocative efficiency, and other related measures, as well as in Capital Assets Pricing Models to analyse the performance of investment portfolios. The project will start by reviewing and extending recent results by Bellini and Di Bernardino (2017) about the asymptotic connection between high population expectiles and their quantile counterparts. The student shall then work on a generalisation of the asymptotic results of Daouia et al. (2018), developing the convergence of so-called indirect (quantile-based) and direct (ALS) extreme expectile estimators, when the underlying distribution is either short-tailed or light-tailed.

Prerequisites: No previous knowledge of expectile theory or extreme value analysis is necessary. The student should have a good background in parametric inference. Coding skills (in R) are desirable but not necessary.

References 

Bellini, F., Di Bernardino, E. (2017). Risk management with expectiles, The European Journal of Finance 23(6): 487-506.

Daouia, A., Girard, S., Stupfler, G. (2018). Estimation of tail risk based on extreme expectiles, Journal of the Royal Statistical Society: Series B 80(2): 263-292.

Daouia, A., Girard, S., Stupfler, G. (2020). Tail expectile process and risk assessment, Bernoulli 26(1): 531-556.

Newey, W.K., Powell, J.L. (1987). Asymmetric least squares estimation and testing, Econometrica 55(4): 819-847.