Journal article
A NOTE ON NONPARAMETRIC ESTIMATION OF THE CTE
ASTIN bulletin, Vol.39(2), pp.717-734
11/01/2009
DOI: 10.2143/AST.39.2.2044655
Abstract
The alpha-level Conditional Tail Expectation (CTE) of a continuous random variable X is defined as its conditional expectation given the event {X> q(alpha)} where q(alpha) represents its alpha-level quantile. It is well known that the empirical CTE (the average of the n (1-alpha) largest order statistics in a sample of size n) is a negatively biased estimator of the CTE. This bias vanishes as the sample size increases, but in small samples can be significant. In this article it is shown that an unbiased nonparametric estimator of the CTE does not exist. In addition, the asymptotic behavior of the bias of the empirical CTE is studied, and a closed form expression for its first order term is derived. This expression facilitates the study of the behavior of the empirical CTE with respect to the underlying distribution, and suggests an alternative (to the bootstrap) approach to bias correction. The performance of the resulting estimator is assessed via simulation.
Details
- Title: Subtitle
- A NOTE ON NONPARAMETRIC ESTIMATION OF THE CTE
- Creators
- Bangwon Ko - Soongsil UniversityRalph P Russo - University of IowaNariankadu D Shyamalkumar - University of Iowa
- Resource Type
- Journal article
- Publication Details
- ASTIN bulletin, Vol.39(2), pp.717-734
- Publisher
- CAMBRIDGE UNIV PRESS
- DOI
- 10.2143/AST.39.2.2044655
- ISSN
- 0515-0361
- eISSN
- 1783-1350
- Number of pages
- 18
- Grant note
- DMS 06-18883 / National Science Foundation
- Language
- English
- Date published
- 11/01/2009
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257631702771
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