Functional kernel estimators of large conditional quantiles

Scandinavian J Statistics

Girard

2014

Self Cite

In this paper, we introduce a new risk measure, the so‐called conditional tail moment. It is defined as the moment of order a ≥ 0 of the loss distribution above the upper α‐quantile where α ∈ (0,1). Estimating the conditional tail moment permits us to estimate all risk measures based on conditional moments such as conditional tail expectation, conditional value at risk or conditional tail variance. Here, we focus on the estimation of these risk measures in case of extreme losses (where α ↓0 is no longer fixed). It is moreover assumed that the loss distribution is heavy tailed and depends on a covariate. The estimation method thus combines non‐parametric kernel methods with extreme‐value statistics. The asymptotic distribution of the estimators is established, and their finite‐sample behaviour is illustrated both on simulated data and on a real data set of daily rainfalls.

((), RVaR (α_{n} MathClass-rel| x) MathClass-punc, {RCTM}_{1} (α_{n} MathClass-rel| x) MathClass-punc, {RCTM}_{2} (α_{n} MathClass-rel| x) MathClass-punc, {RCTM}_{3} (α_{n} MathClass-rel| x)) .

…”

Section: The Regression Conditional Tail Moment: Definition and Estimmentioning

confidence: 99%

Non‐parametric Estimation of Extreme Risk Measures from Conditional Heavy‐tailed Distributions

Methni

Scandinavian J Statistics

Girard

2014

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“…In Davison and Ramesh [10], a local likelihood smoothing procedure is considered for the estimation of a conditional generalized extreme value distribution and Eastoe and Tawn [12] propose to model the covariate effect by a Box-Cox location-scale model. A nonparametric estimation procedure is proposed by Daouia et al ([7] and [8]) and Gardes and Girard [18].…”

Section: Introductionmentioning

confidence: 99%

Tail dimension reduction for extreme quantile estimation

2017

Extremes

Self Cite

In a regression context where a response variable Y ∈ R is recorded with a covariate X ∈ R p , two situations can occur simultaneously: (a) we are interested in the tail of the conditional distribution and not on the central part of the distribution and (b) the number p of regressors is large. To our knowledge, these two situations have only been considered separately in the literature. The aim of this paper is to propose a new dimension reduction approach adapted to the tail of the distribution in order to propose an efficient conditional extreme quantile estimator when the dimension p is large. The results are illustrated on simulated data and on a real dataset.

“…Here γ (x 0 ) is referred to as the conditional extreme value index at point x 0 . Its estimation has been considered for instance in Daouia et al (2013) and Gardes and Girard (2012). An adaption of the moment estimator has been proposed in and Stupfler (2013) and a maximum likelihood approach was considered by Wang and Tsai (2009).…”

Section: Introductionmentioning

confidence: 99%

A general estimator for the extreme value index: applications to conditional and heteroscedastic extremes

2015

Extremes

Self Cite

The tail behavior of a survival function is controlled by the extreme value index. The aim of this paper is to propose a general procedure for the estimation of this parameter in the case where the observations are not necessarily distributed from the same distribution. The idea is to estimate in a consistent way the survival function and to apply a general functional to obtain a consistent estimator for the extreme value index. This procedure permits to deal with a large set of models such as conditional extremes and heteroscedastic extremes. The consistency of the obtained estimator is established under general conditions. A simulation study and a concrete application on financial data are proposed to illustrate the finite sample behavior of the proposed procedure.