Stéphane Girard

Stéphane Girard
Senior research scientist at Inria Grenoble Rhône-Alpes.

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Extremes

High dimensional statistical learning

Applications

Boundary or frontier estimation, and more generally, level sets estimation, are recurrent functional estimation problems in statistics which are linked to outlier detection. In biology, one is interested in estimating reference curves, that it to say curves which bound 90% (for instance) of the population. Points outside this bound are considered as outliers compared to the reference population. Here, reference curves are computed through nonparametric regression quantile estimations (see Figure 1).

Figure 1: Reference curves for a given women population. The sebum rate measured on the forhead of each is woman is reported against the age. The curves represent various nonparametric estimates of the 10% reference curves bounding 90% of the population.

extreme quantiles approach

asymptotic distribution of the error

linear programming approach

Figure 2: Boundary estimation using a linear programming approach: blue points (dots) are data points, the dot curve is the unknown boundary, the continuous curve is the estimated boundary, the square points are points on the estimated boundary and the triangle points are the additional points actually used in the estimation (support vectors).

PhD theseshere

G. Stupfler "Un modèle de Markov caché en assurance et Estimation de frontière et de point terminal", Université de Strasbourg, novembre 2011 [pdf].

A. Lekina, " Estimation non-paramétrique des quantiles extrêmes conditionnels , Université Grenoble 1, octobre 2010 [pdf].

L. Gardes, "Estimation d'une fonction quantile extrême", Université Montpellier 2, octobre 2003 [pdf].

Frontier estimation with linear programming methods

A. Nazin & S. Girard. "L1-optimal linear programming estimator for periodic frontier functions with Holder continuous derivative", Automation and Remote Control, 75(12), 2152-2169, 2014. [Associated technical report: pdf].

G. Bouchard, S. Girard, A. Iouditski & A. Nazin. "Some linear programming methods for frontier estimation", Applied Stochastic Models in Business and Industry, 21(2), 175-185, 2005.

S. Girard, A. Iouditski & A. Nazin. "L1-optimal frontier estimation via linear programming", Automation and Remote Control, 66(12), 2000-2018, 2005. [Associated technical report: ps/pdf or pdf].

G. Bouchard, S. Girard, A. Iouditski & A. Nazin. "Nonparametric estimation of the support boundary through linear programming", Automation and Remote Control, 65(1), 58-64, 2004. [Associated technical report: ps/pdf or ps].

Nonparametric regression on extreme observations

S. Girard, G. Stupfler & A. Usseglio-Carleve, "Functional estimation of extreme conditional expectiles", Econometrics and Statistics, 21, 131--158, 2022. [Associated technical report: pdf].

S. Girard, G. Stupfler & A. Usseglio-Carleve, "Extreme Lp-quantile kernel regression", In Advances in Contemporary Statistics and Econometrics, A. Daouia and A. Ruiz-Gazen (eds.), Springer, 197-219, 2021. [Associated technical report:pdf].

A. Ag Ahmad, E. Deme, A. Diop & S. Girard. "Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions", Dependence Modeling, 7, 394--417, 2019 [associated technical report: pdf].

J. El Methni, L. Gardes & S. Girard. "Kernel estimation of extreme regression risk measures", Electronic Journal of Statistics, 12, 359--398, 2018. [associated technical report: pdf].

L. Gardes & S. Girard. "On the estimation of the functional Weibull tail-coefficient", Journal of Multivariate Analysis, 146, 24--45, 2016. [associated technical report: pdf].

S. Girard & S. Louhichi "On the strong consistency of the kernel estimator of extreme conditional quantiles", In E. Ould-Said et al, editors, Functional Statistics and Applications, Springer, pages 59--77, 2015. [associated technical report: pdf].

J. El Methni, L. Gardes & S. Girard. "Nonparametric estimation of extreme risk measures from conditional heavy-tailed distributions", Scandinavian Journal of Statistics, 41, 988--1012, 2014. [associated technical report: pdf].

A. Daouia, L. Gardes & S. Girard. "On kernel smoothing for extremal quantile regression", Bernoulli, 19, 2557--2589, 2013. [associated technical report: pdf].

L. Gardes & S. Girard. "Functional kernel estimators of large conditional quantiles", Electronic Journal of Statistics, 6, 1715--1744, 2012. [associated technical report: pdf].

J. Carreau & S. Girard. "Spatial extreme quantile estimation using a weighted log-likelihood approach", Journal de la Société Française de Statistique, 152(3), 66--83, 2011.

L. Gardes & S. Girard "Functional kernel estimators of conditional extreme quantiles" In F. Ferraty, editor, Recent advances in functional data analysis and related topics, pages 135-140, Springer, Physica-Verlag, 2011. [Associated technical report: pdf].

A. Daouia, L. Gardes, S. Girard & A. Lekina. "Kernel estimators of extreme level curves", Test, 20(2), 311--333, 2011. [Associated technical report: pdf].

L. Gardes & S. Girard. "Conditional extremes from heavy-tailed distributions: An application to the estimation of extreme rainfall return levels", Extremes, 13(2), 177--204, 2010. [Associated technical report: pdf].

L. Gardes, S. Girard & A. Lekina. "Functional nonparametric estimation of conditional extreme quantiles", Journal of Multivariate Analysis, 101, 419--433, 2010. [Associated technical report: pdf].

L. Gardes & S. Girard. "A moving window approach for nonparametric estimation of the conditional tail index", Journal of Multivariate Analysis, 99, 2368--2388, 2008. [Associated technical report: pdf].

S. Girard & P. Jacob. "A note on extreme values and kernel estimators of sample boundaries", Statistics and Probability Letters, 64, 982--986, 2008. [Associated technical report: pdf].

S. Girard & L. Menneteau. "Smoothed extreme value estimators of non-uniform point processes boundaries with application to star-shaped supports estimation", Communication in Statistics - Theory and Methods, 37(6), 881--897, 2008. [Associated technical report: pdf].

S. Girard & L. Menneteau. "Central limit theorems for smoothed extreme value estimates of point processes boundaries", Journal of Statistical Planning and Inference, 135(2), 433-460, 2005. [Associated technical report: pdf].

S. Girard & P. Jacob. "Extreme values and kernel estimates of point processes boundaries", ESAIM: Probability and Statistics, 8, 150-168, 2004. [Associated technical report: pdf ps].

S. Girard & P. Jacob. "Projection estimates of point processes boundaries", Journal of Statistical Planning and Inference, 116(1):1-15, 2003. [Associated technical report: pdf ps].

S. Girard & P. Jacob. "Extreme value and Haar series estimates of point process boundaries", Scandinavian Journal of Statistics, 30(2):369-384, 2003. [Associated technical report: pdf ps].