Tail Behavior for the Suprema of Gaussian Processes with a View Towards Empirical Processes.

Abstract

Initially this document considers the standard isonormal linear process L on a Hilbert space H, and applying metric entropy methods obtain bounds for a certain probability. Under the assumption that the entropy function of C grows polynomially, we find bounds of the form where delta squared is the maximal variance of L. We use a notion of entropy finer than that usually employed, and specifically suited to the non-stationary situation. As a result we obtain, in the non-stationary setting, more precise bounds than any in the literature. We then treat a number of examples in which the power alpha is identified. These include the distribution of the maximum of certain locally stationary.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1985
Accession Number
ADA166151

Entities

People

  • Gennady Samorodnitsky
  • Robert J. Adler

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Banach Space
  • Classification
  • Covariance
  • Data Science
  • Gaussian Processes
  • Hilbert Space
  • Information Science
  • North Carolina
  • Probability
  • Random Variables
  • Security
  • Standards
  • Stationary
  • Stationary Processes
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Statistical inference.

Technology Areas

  • Space