Sieves and Signal Extraction.

Abstract

Given a Gaussian signal with known mean and covariance kernel R, and given a second covariance R, the PI has proved several results concerning the probability that the sample path of the signal will fall in the reproducing kernal Hilbert space with kernal R. This is applied to optimal extraction of an unobservable signal based on its conditional mean, and to generalization of a zero-one law given by Kallianpur and by Driscoll. For an observable Gaussian process with unknown mean and covariance, an extension of previous work shows that simultaneous consistent estimation of both the mean and the covariance is possible by the method of sieves. In both this and the signal extraction problem, no assumption is made about the nature of the time parameter of the process. Some work on the axiomatic theory of confounding in experimental designs is also reported.

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Document Details

Document Type
Technical Report
Publication Date
Oct 29, 1986
Accession Number
ADA177628

Entities

People

  • Jay H. Beder

Organizations

  • University of Wisconsin–Milwaukee

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Availability
  • Classification
  • Covariance
  • Data Science
  • Experimental Design
  • Extraction
  • Gaussian Processes
  • Hilbert Space
  • Inequalities
  • Information Science
  • Law
  • Mathematics
  • Probability
  • Security
  • Statistical Analysis
  • Statistics
  • Stochastic Processes

Readers

  • Research Science/Academic Research
  • Statistical inference.

Technology Areas

  • Space