Likelihood-based Inference under Non-Convex Boundary Constraints

Music City Center 

Likelihood-based inference under non-convex 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 non-convex parameter space. We further derive the asymptotic distribution of the likelihood ratio test statistic under non-convex 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.

Likelihood ratio test

Metric projection

Non-standard condition 

Biometrics Section