DeepAI AI Chat
Log In Sign Up

On the Bias of the Score Function of Finite Mixture Models

by   Rodrigo Labouriau, et al.

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.


page 1

page 2

page 3

page 4


On The Identifiability of Mixture Models from Grouped Samples

Finite mixture models are statistical models which appear in many proble...

An Operator Theoretic Approach to Nonparametric Mixture Models

When estimating finite mixture models, it is common to make assumptions ...

Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations

Recent research has established sufficient conditions for finite mixture...

Estimating the Number of Components in Finite Mixture Models via the Group-Sort-Fuse Procedure

Estimation of the number of components (or order) of a finite mixture mo...

On Coarse Graining of Information and Its Application to Pattern Recognition

We propose a method based on finite mixture models for classifying a set...

Exact fit of simple finite mixture models

How to forecast next year's portfolio-wide credit default rate based on ...