TY - JOUR
T1 - On the Bias of the Score Function of Finite Mixture Models
AU - Labouriau, Rodrigo
PY - 2023/5
Y1 - 2023/5
N2 - 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.
AB - 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.
KW - Finite-mixture-models
KW - inference-functions
KW - score-function
KW - semiparametric- models
UR - http://www.scopus.com/inward/record.url?scp=85118255653&partnerID=8YFLogxK
U2 - 10.1080/03610926.2021.1995429
DO - 10.1080/03610926.2021.1995429
M3 - Journal article
SN - 0361-0926
VL - 52
SP - 4461
EP - 4467
JO - Communications in Statistics: Theory and Methods
JF - Communications in Statistics: Theory and Methods
IS - 13
ER -