Bias and Variance Approximations for Estimators of Extreme Quantiles

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1988
Accession Number
ADA204930

Entities

People

  • Richard L. Smith

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Distribution Functions
  • Estimators
  • Families (Human)
  • Mathematics
  • Maximum Likelihood Estimation
  • Normal Distribution
  • North Carolina
  • Numbers
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Algorithms
  • Statistical Inference
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.
  • Statistical inference.