Asymptotic properties of a stochastic EM Algorithm for estimating mixing proportions
- 1 January 1993
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics. Stochastic Models
- Vol. 9 (4) , 599-613
- https://doi.org/10.1080/15326349308807283
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 as the sample size N tends to infinity, the stationary distribution of the ergodic Markov chain generated by SEM converges to a Gaussian distribution whose mean is the consistent maximum likelihood estimate of p:. The asymptotic variance is proportional to N -1Keywords
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