Non‐parametric Estimation of Extreme Risk Measures from Conditional Heavy‐tailed Distributions. (18th February 2014)

• Record Type: Journal Article
• Authors: Methni, Jonathan El; Gardes, Laurent; Girard, Stéphane
• Is Part Of: Scandinavian journal of statistics. Volume 41:Number 4(2014:Dec.)
• Page Start: 988
• Page End: 1012
• Publication Date: 2014-02-18
• Subjects: Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12078
• Languages: English
• ISSNs: 0303-6898

Abstract

<abstract abstract-type="main" id="sjos12078-abs-0001"> <title>ABSTRACT</title> <p>In this paper, we introduce a new risk measure, the so‐called conditional tail moment. It is defined as the moment of order <italic>a</italic> ≥ 0 of the loss distribution above the upper <italic>α</italic>‐quantile where <italic>α</italic> ∈ (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 <italic>α ↓</italic>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.</p> </abstract>