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

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

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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.

Originalsprog	Engelsk
Tidsskrift	Communications in Statistics: Theory and Methods
Vol/bind	52
Nummer	13
Sider (fra-til)	4461-4467
Antal sider	7
ISSN	0361-0926
DOI	https://doi.org/10.1080/03610926.2021.1995429
Status	Udgivet - maj 2023

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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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