統計学輪講（第27回）

    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.