Large Deviations for the Maxima of Some Random Fields.

Abstract

Several statistical problems which involve the distribution of the maximum of Gaussian random fields are described. Specific examples are the pinned Brownian sheet and a Brownian bridge with 'reflection', which arises in certain change point problems. In these concrete cases the method of Pickands (1969, Trans. Amer. Math. Soc.) is adapted to give large deviation probabilities for the maximum, both for continuous and for discrete indexing sets. A different method is used to give a second order correction for the reflected Brownian bridge and hence for reflected Brownian motion. The numerical accuracy of the approximations is studied via simulation.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1985
Accession Number
ADA155909

Entities

People

  • David Siegmund
  • M. L. Hogan

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Brownian Motion
  • Covariance
  • Data Science
  • Distribution Functions
  • Gaussian Processes
  • Information Science
  • Military Research
  • Probability
  • Probability Density Functions
  • Random Variables
  • Random Walk
  • Sequential Analysis
  • Statistical Tests
  • Statistics
  • Stochastic Processes
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Plasma Physics / Magnetohydrodynamics
  • Statistical inference.