統計学輪講（第２回）

統計学輪講（第2回）
日時      2013年04月16日(火)    14時50分～16時30分
場所      経済学部新棟３階第３教室
講演者     下津 克己（経済）
演題：Testing the Number of Components in Finite Mixture Econometric Models

概要
We consider likelihood-based testing of the null hypothesis of m components against
the alternative of m+1 components in a finite mixture model. The number of components is
an important parameter in the applications of finite mixture models. Still, testing the number
of components has been a long-standing challenging problem because of its non-regularity.
The likelihood ratio test (LRT) statistic converges to a supremum of the square of a Gaussian
process in distribution, but implementing the LRT is difficult because of computational and
technical issues such as non-finite variance.
We propose a likelihood-based testing procedure of the number of components. The proposed test,
extending the EM approach of Li, Chen and Marriott (2009), does not use a penalty term and is
implementable even when the LRT is difficult to implement. Simulations show that the proposed
test has good finite sample size and power properties.