NONPARAMETRIC ESTIMATION IN MARKOV PROCESSES.

Abstract

The purpose of the present paper is to consider the non-parametric estimation of densities in the case of Markov processes. Asymptotically unbiased estimates for the initial and (two-dimensional) joint densities are constructed. These estimates are shown to be consistent in quadratic mean, and furthermore a consistent, in the probability sense, estimate for the transition density is obtained. It is shown that, under suitable conditions, all three estimators mentioned, properly normalized, are asymptotically normal.

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1967
Accession Number
AD0653272

Entities

People

  • George C. Roussas

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Estimators
  • Markov Processes
  • Mathematics
  • Probability
  • Random Variables
  • Stochastic Processes
  • Transitions
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Statistical inference.