Mixture inference at the edge of identifiability

Daeyoung Kim
Department of Statistics
Penn State University
ABSTRACT:
Identifiability is a principal assumption of statistical models in order to make meaningful inferences. There are two nonidentifiabilities in finite mixture models: boundary nonidentifiability and label nonidentifiability. Although pa- rameters are not identifiable in the strict sense, there is a form of asymptotic identifiability which can provide reasonable answers when components densi- ties are well separated, relative to the sample size. Asymptotic identifiability is related to local identifiability. In this talk, we examine the role of the two key identifiabilities and nonidentifiabilities on finite mixture inference, and investi- gate estimation and labelling of parameter estimators when the identifiability of the finite mixture model is weak, relative to the sample size. We then propose new methods which can solve several drawbacks of existing methods.