On the Bias of the Score Function of Finite Mixture Models

Rodrigo Labouriau

doi:10.1080/03610926.2021.1995429

On the Bias of the Score Function of Finite Mixture Models

Department of Mathematics

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Abstract

We characterise the unbiasedness of the score function, viewed as an inference function for a class of finite mixture models. The models studied represent the situation where there is a stratification of the observations in a finite number of groups. We show that, under mild regularity conditions, the score function for estimating the parameters identifying each group's distribution is unbiased. We also show that if one introduces a mixture in the scenario described above, so that for some observations it is only known that they belong to some of the groups with a probability not in larger than 0 and smaller than 1, then the score function becomes biased. We argue then that under further mild regularity, the maximum likelihood estimate is not consistent. The results above are extended to regular models containing arbitrary nuisance parameters, including semiparametric models.

Original language	English
Journal	Communications in Statistics: Theory and Methods
Volume	52
Issue	13
Pages (from-to)	4461-4467
Number of pages	7
ISSN	0361-0926
DOIs	https://doi.org/10.1080/03610926.2021.1995429
Publication status	Published - May 2023

Keywords

Finite-mixture-models
inference-functions
score-function
semiparametric- models

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10.1080/03610926.2021.1995429

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On the Bias of the Score Function of Finite Mixture Models

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