ASYMPTOTIC NORMALITY OF CERTAIN FUNCTIONS DEFINED ON A MARKOV PROCESS.

Abstract

In the present paper it is first proved that, under essentially the same conditions, the quotients (summation from m=1 to m-n of g sub m/summation from m=1 to m=n of f sub m) and (summation from m=1 to m=n of f sub m/summation from m=1 to m=n of g sub m) properly normalized, are also asymptotically normal. Next, the functions f and g are also considered to be dependent on n--the number of the random variables X sub j, j=1,...,n--and asymptotic normalities similar to the ones mentioned above are established under a number of conditions. The results obtained here are useful in statistical applications and are applied in the problem of non-parametric estimation in Markov processes.

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1967
Accession Number
AD0653271

Entities

People

  • George G. Roussas

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Computing-Related Activities
  • Data Science
  • Information Science
  • Interdisciplinary Science
  • Markov Processes
  • Mathematical Analysis
  • Mathematics
  • Normality
  • Probability
  • Random Variables

Fields of Study

  • Mathematics

Readers

  • Climatology
  • Computational Modeling and Simulation
  • Graph Algorithms and Convex Optimization.