The objective of extremal regression is to estimate and infer quantities describing the tail of a conditional distribution. Examples of such quantities include quantiles and expectiles, and the regression version of the Expected Shortfall. Traditional regression estimators at the tails typically suffer from instability and inconsistency due to data sparseness, especially when the underlying conditional distributions are heavy-tailed. Existing approaches to extremal regression in the heavy-tailed case fall into two main categories: linear quantile regression approaches and, at the opposite, nonparametric approaches. They are also typically restricted to i.i.d. data-generating processes. I will here give an overview of a recent series of papers that discuss extremal regression methods in location-scale regression models (containing linear regression quantile models) and nonparametric regression models. Some key novel results include a general toolbox for extreme value estimation in the presence of random errors and joint asymptotic normality results for nonparametric extreme conditional quantile estimators constructed upon strongly mixing data. Joint work with A. Daouia, S. Girard, M. Oesting and A. Usseglio-Carleve.
Références : Girard, S., Stupfler, G. and Usseglio-Carleve, A. (2021). Extreme conditional expectile estimation in heavy-tailed heteroscedastic regression models, Annals of Statistics 49(6): 3358-3382. Daouia, A., Stupfler, G. and Usseglio-Carleve, A. (2023). Inference for extremal regression with dependent heavy-tailed data, Annals of Statistics 51(5): 2040-2066.
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