https://orcid.org/0000-0003-0835-0788
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J Y Wang, Z S Ye, Y Chen, Likelihood-based inference under nonconvex boundary constraints, Biometrika, Volume 111, Issue 2, June 2024, Pages 591–607, https://doi.org/10.1093/biomet/asad062
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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.
