A diagnostic tool for mixture models

Abstract

Mixture models are used in a large number of applications yet there remain difficulties with maximum likelihood estimation. For instance, the likelihood surface for finite normal mixtures often has a large number of local maximizers, some of which do not give a good representation of the underlying features of the data. In this paper we present diagnostics that can be used to check the quality of an estimated mixture distribution. Particular attention is given to normal mixture models since they frequently arise in practice. We use the diagnostic tools for finite normal mixture problems and in the nonparametric setting where the difficult problem of determining a scale parameter for a normal mixture density estimate is considered. A large sample justification for the proposed methodology will be provided and we illustrate its implementation through several examples

Keywords:

• Density estimation
• Diagnostics
• Mixture model
• Residuals