Download or read book Bias and Variance Approximations for Estimators of Extreme Quantiles written by Richard L. Smith and published by . This book was released on 1988 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most techniques for estimating extreme values are based on the assumption of a parametric family motivated by extreme value limit theory. This creates two sources of estimation error: The ordinary estimation variance and a bias created by mis-specification of a parametric model. In this paper approximate formulae are derived for the bias and variance of four widely studied estimators. This allows comparison among the different estimators. The development relies on recent work on probabilistic approximations in extreme value theory. Keywords: Extreme values; Generalized extreme value distribution; Generalized pareto distribution; Gumbel distribution; Maximum likelihood; Threshold methods. (jhd).