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An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, 2The problem of obtaining numerically maximum likelihood estimates of the parameters for a mixture of normal distributions is addressed. In recent literature, a certain successive approximations procedure, based on the likelihood equations, is shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, a general iterative procedure is introduced, 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. With probability 1 as the sample size grows large, it is shown that this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. 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
19760019841
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Peters, B. C., Jr. (Houston Univ. TX, United States)
Walker, H. F. (Houston Univ. TX, United States)
Date Acquired
September 3, 2013
Publication Date
February 1, 1976
Subject Category
Statistics And Probability
Report/Patent Number
NASA-CR-147739
REPT-51
Accession Number
76N26929
Funding Number(s)
CONTRACT_GRANT: NAS9-12777
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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