Hypothesis testing in mixture regression models

• 成果类型: Article
• 署名作者: Zhu, HT; Zhang, HP
• 署名单位: Yale University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1046/j.1369-7412.2003.05379.x
• 发表日期: 2004
• 页码: 3-16
• 关键词: likelihood ratio test; quantitative trait; homogeneity; parameter

摘要

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.