An approximation to the information matrix of exponential family finite mixtures

Andrew M. Raim (), Nagaraj K. Neerchal and Jorge G. Morel
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Andrew M. Raim: University of Maryland, Baltimore County
Nagaraj K. Neerchal: University of Maryland, Baltimore County
Jorge G. Morel: University of Maryland, Baltimore County

Annals of the Institute of Statistical Mathematics, 2017, vol. 69, issue 2, No 4, 333-364

Abstract: Abstract A simple closed form of the Fisher information matrix (FIM) usually cannot be obtained under a finite mixture. Several authors have considered a block-diagonal FIM approximation for binomial and multinomial finite mixtures, used in scoring and in demonstrating relative efficiency of proposed estimators. Raim et al. (Stat Methodol 18:115–130, 2014a) noted that this approximation coincides with the complete data FIM of the observed data and latent mixing process jointly. It can, therefore, be formulated for a wide variety of missing data problems. Multinomial mixtures feature a number of trials, which, when taken to infinity, result in the FIM and approximation becoming arbitrarily close. This work considers a clustered sampling scheme which allows the convergence result to be extended significantly to the class of exponential family finite mixtures. A series of examples demonstrate the convergence result and suggest that it can be further generalized.

Keywords: Fisher information; Complete data; Clustered sampling; Misclassification rate (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10463-015-0542-9

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