Asymptotic Properties of a Stochastic EM Algorithm for Estimating Mixing Proportions

Abstract

The purpose of this paper is to study the asymptotic behavior of the Stochastic EM algorithm (SEM) in a simple particular case within the mixture context. We consider the estimation of the mixing proportion p of a two- component mixture of densities assumed to be known. We establish that the stationary distribution of the ergodic Markov chain generated by SEM is asymptotic, as the sample size N tends to infinity, to a Gaussian distribution with mean the consistent maximum likelihood estimate of p and variance proportional to N-1/2. Similarly, we determine the limiting distributions of two sequential versions of SEM and study their asymptotic relative efficiency.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1991
Accession Number
ADA246263

Entities

People

  • Gilles Celeux
  • Jean Diebolt

Organizations

  • University of Washington

Tags

Communities of Interest

  • Ground and Sea Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Data Analysis
  • Data Science
  • Distribution Functions
  • Estimators
  • Gaussian Distributions
  • Gaussian Processes
  • Information Science
  • Information Theory
  • Markov Chains
  • Optimal Estimators
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Statistical inference.