A NOTE ON NONPARAMETRIC ESTIMATION OF THE CTE
- Authors
- Ko, Bangwon; Russo, Ralph P.; Shyamalkumar, Nariankadu D.
- Issue Date
- Nov-2009
- Publisher
- PEETERS
- Citation
- ASTIN BULLETIN, v.39, no.2, pp.717 - 734
- Journal Title
- ASTIN BULLETIN
- Volume
- 39
- Number
- 2
- Start Page
- 717
- End Page
- 734
- URI
- http://scholarworks.bwise.kr/ssu/handle/2018.sw.ssu/15751
- DOI
- 10.2143/AST.39.2.2044655
- ISSN
- 0515-0361
- 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.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Natural Sciences > ETC > 1. Journal Articles
![qrcode](https://api.qrserver.com/v1/create-qr-code/?size=55x55&data=https://scholarworks.bwise.kr/ssu/handle/2018.sw.ssu/15751)
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.