Journal article
Bounds for the bias of the empirical CTE
Insurance, mathematics & economics, Vol.47(3), pp.352-357
12/01/2010
DOI: 10.1016/j.insmatheco.2010.08.001
Abstract
The Conditional Tail Expectation (CTE) is gaining an increasing level of attention as a measure of risk It is known that nonparametric unbiased estimators of the CTE do not exist and that CTEn alpha the empirical a-level CTE (the average of the n(1 - alpha) largest order statistics in a random sample of size n) is negatively biased In this article we show that increasing convex order among distributions is preserved by E(CTEn alpha) From this result it is possible to identify the specific distributions within some large classes of distributions that maximize the bias of CTEn alpha This in turn leads to best possible bounds on the bias under various sets of conditions on the sampling distribution F In particular we show that when the alpha-level quantile is an isolated point in the support of a non-degenerate distribution (for example a lattice distribution) then the bias is either of the order 1/root n or vanishes exponentially fast This is intriguing as the bias of CTEn alpha vanishes at the in-between rate of 1/n when F possesses a positive derivative at the alpha th quantile (C) 2010 Elsevier B V All rights reserved
Details
- Title: Subtitle
- Bounds for the bias of the empirical CTE
- Creators
- Ralph P Russo - University of IowaNariankadu D Shyamalkumar - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Insurance, mathematics & economics, Vol.47(3), pp.352-357
- Publisher
- ELSEVIER SCIENCE BV
- DOI
- 10.1016/j.insmatheco.2010.08.001
- ISSN
- 0167-6687
- eISSN
- 1873-5959
- Number of pages
- 6
- Language
- English
- Date published
- 12/01/2010
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257737602771
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