Tail and Quantile Estimation for Strongly Mixing Stationary Sequences

Abstract

This paper primarily concerns the estimation of tail parameters for the marginal distribution F of the terms of a strongly mixing stationary sequence when 1-F(t) decreases exponentially, or is regularly varying as t infinity. The asymptotic properties of the Hill estimator for the exponential parameter or regular variation index are developed within this framework. Estimation procedures are investigated for tail probabilities and tail quantiles, both for the individual terms of the process and for their maxima over groups of consecutive terms. The latter case requires estimation of the so called extremal index, and substantially involves the local dependence structure of the sequence.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1990
Accession Number
ADA223472

Entities

People

  • Holger Rootzen
  • Laurens De Haan
  • M. Ross Leadbetter

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Data Science
  • Differential Equations
  • Distribution Functions
  • Equations
  • Estimators
  • Hilbert Space
  • Information Science
  • Integrals
  • Mathematical Filters
  • Normality
  • North Carolina
  • Order Statistics
  • Probability
  • Random Variables
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Regression Analysis.