Model selection of Gaussian mixture process and its application

In this article, new penalized likelihood methods are proposed for model selection of Gaussian mixture process. Our methods integrate functional principal component analysis, kernel density regression, and penalized estimation, which can be carried out by EM algorithms. Component selection and parameter estimation are conducted simultaneously. Monte Carlo simulation shows that our methods require less computation and have accurate estimation even with not well separated data. The methods are further applied to a supermarket customer flow data to reveal some interesting patterns of shopping behavior.