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An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributionsThis paper addresses the problem of obtaining numerically maximum-likelihood estimates of the parameters for a mixture of normal distributions. In recent literature, a certain successive-approximations procedure, based on the likelihood equations, was shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, we introduce a general iterative procedure, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. We show that, with probability 1 as the sample size grows large, this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. We also show that the step-size which yields optimal local convergence rates for large samples is determined in a sense by the 'separation' of the component normal densities and is bounded below by a number between 1 and 2.
Document ID
19780065084
Document Type
Reprint (Version printed in journal)
Authors
Peters, B. C., Jr. (Houston Univ. TX, United States)
Walker, H. F. (Houston, University Houston, Tex., United States)
Date Acquired
August 9, 2013
Publication Date
September 1, 1978
Publication Information
Publication: SIAM Journal on Applied Mathematics
Volume: 35
Subject Category
STATISTICS AND PROBABILITY
Funding Number(s)
CONTRACT_GRANT: NAS9-12777
Distribution Limits
Public
Copyright
Other