Likelihood-based inference under nonconvex boundary constraints

J Y Wang, Z S Ye and Y Chen

Biometrika, 2024, vol. 111, issue 2, 591-607

Abstract: 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.

Keywords: Likelihood ratio test; Metric projection; Nonstandard condition (search for similar items in EconPapers)
Date: 2024
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