Likelihood-based inference under nonconvex boundary constraints

• 成果类型: Article
• 署名作者: Wang, J. Y.; Ye, Z. S.; Chen, Y.
• 署名单位: National University of Singapore; University of Pennsylvania
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad062
• 发表日期: 2024
• 关键词: ratio tests; associations; statistics; regression; variants

摘要

Likelihood-based inference under nonconvex constraints on model parameters has become increasingly common in biomedical research. In this paper, we establish large-sample properties of the maximum likelihood estimator when the true parameter value lies at the boundary of a nonconvex parameter space. We further derive the asymptotic distribution of the likelihood ratio test statistic under nonconvex constraints on model parameters. A general Monte Carlo procedure for generating the limiting distribution is provided. The theoretical results are demonstrated by five examples in Anderson's stereotype logistic regression model, genetic association studies, gene-environment interaction tests, cost-constrained linear regression and fairness-constrained linear regression.