統計学輪講（第27回） 日時 2018年01月09日(火) 14時55分～16時35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 正規混合モデルに関連する統計モデル 概要 In this talk, I discuss two models related to normal mixture models. 1. Likelihood ratio test for logistic-normal mixture model (with Yoichi Arai and Hiroyuki Kasahara) In clinical trials, it is useful to find out a subgroup of patients with certain attributes who can benefit from a treatment. Shen and He (2015) propose to use a logistic-normal mixture modelfor subgroup identification, where the treatment effect for each group follows a Gaussian linear model and the mixing proportions is a logistic function of the covariates. In subgroup identification, it is important to test the existence of subgroups with differential treatment effects, but the asymptotic distribution of the likelihood ratio test statistic has been unknown because of irregular structure of a logistic-normal mixture model. Shen and He (2015) develop an EM test of the existence of subgroups that sidesteps this difficulty. We propose to use the likelihood ratio test of the existence of subgroups and derive its asymptotic distribution. Our simulation results show that the likelihood ratio test has better power than the EM test of Shen and He (2015). Shen, J. and He, X. (2015), "Inference for Subgroup Analysis With a Structured Logistic-Normal Mixture Model," Journal of the American Statistical Association, 110, 303-312. 2. Testing the Number of Regimes in Markov Regime Switching Models (with Hiroyuki Kasahara) Markov regime switching models have been used in numerous empirical studies in economics and finance. However, the asymptotic distribution of the likelihood ratio test statistic for testing the number of regimes in Markov regime switching models has been an unresolved problem. We derive the asymptotic distribution of the likelihood ratio test statistic for testing the null hypothesis of M regimes against the alternative hypothesis of M+1 regimes for any M>=1 both under the null hypothesis and under local alternatives. We show that the contiguous alternatives converge to the null hypothesis at a rate of n^(-1/8) in regime switching models with normal density. Asymptotic validity of parametric bootstrap is also established.