A Sieve Estimator for the Covariance of a Gaussian Process.

Abstract

Maximum likelihood estimation for the covariance R of a zero-mean Gaussian process is considered, with no assumptions on the covariance or the time parameter set T. It is shown that the likelihood function is a.s. unbounded in general, and a sieve estimator R is constructed. The distribution of R, considered as a process on TxT, can be described exactly if a certain technical assumption is satisfied concerning the bivariate series expansion of R. It is then shown that R (s,t) is asymptotically unbiased and consistent (weakly and in mean square) at each (s,t) is an element of TxT, and that R is strongly consistent (globally) in an appropriate norm.

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1987
Accession Number
ADA177560

Entities

People

  • Jay H. Beder

Organizations

  • University of Wisconsin–Milwaukee

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Covariance
  • Data Science
  • Estimators
  • Gaussian Processes
  • Information Science
  • Mathematical Analysis
  • Mathematics
  • Maximum Likelihood Estimation
  • Optimal Estimators
  • Statistical Algorithms
  • Statistical Analysis

Fields of Study

  • Mathematics

Readers

  • Statistical inference.