On the Bias of the Score Function of Finite Mixture Models

02/09/2020
by   Rodrigo Labouriau, et al.
0

We characterize 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 if the observations belonging to the same group follow the same distribution and the K distributions associated with each group are distinct elements of a sufficiently regular parametric family of probability measures, then the score function for estimating the parameters identifying the distribution of each group is unbiased. However, 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 given probability (not all in 0, 1), then the score function becomes biased. We argue then that under further mild regularity conditions, the maximum likelihood estimate is not consistent.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset