Premium
Hypothesis testing in mixture regression models
Author(s) -
Zhu HongTu,
Zhang Heping
Publication year - 2004
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1046/j.1369-7412.2003.05379.x
Subject(s) - mathematics , statistics , m estimator , homogeneity (statistics) , likelihood principle , estimator , restricted maximum likelihood , likelihood ratio test , score test , resampling , maximum likelihood , statistical hypothesis testing , asymptotic distribution , regression analysis , likelihood function , empirical likelihood , maximum likelihood sequence estimation , expectation–maximization algorithm , quasi maximum likelihood
Summary. We establish asymptotic theory for both the maximum likelihood and the maximum modified likelihood estimators in mixture regression models. Moreover, under specific and reasonable conditions, we show that the optimal convergence rate of n −1/4 for estimating the mixing distribution is achievable for both the maximum likelihood and the maximum modified likelihood estimators. We also derive the asymptotic distributions of two log‐likelihood ratio test statistics for testing homogeneity and we propose a resampling procedure for approximating the p ‐value. Simulation studies are conducted to investigate the empirical performance of the two test statistics. Finally, two real data sets are analysed to illustrate the application of our theoretical results.