Likelihood-based inference under nonconvex boundary constraints.

Area of Science:

• Statistics
• Biomedical Research
• Econometrics

Background:

• Likelihood-based inference is crucial in biomedical research.
• Nonconvex constraints on model parameters are increasingly common.
• Challenges arise when true parameter values lie at the boundary of these constraints.

Purpose of the Study:

• Establish large-sample properties of the maximum likelihood estimator under boundary conditions in nonconvex parameter spaces.
• Derive the asymptotic distribution of the likelihood ratio test statistic under such constraints.
• Provide a general Monte Carlo procedure for generating the limiting distribution.

Main Methods:

• Asymptotic theory for maximum likelihood estimation.
• Derivation of the asymptotic distribution for the likelihood ratio test statistic.
• Development of a Monte Carlo simulation procedure for the limiting distribution.

Main Results:

• Established large-sample properties of the maximum likelihood estimator at the boundary of nonconvex parameter spaces.
• Derived the asymptotic distribution of the likelihood ratio test statistic under nonconvex constraints.
• Demonstrated the applicability of the methods through five diverse examples.

Conclusions:

• The study provides essential theoretical tools for likelihood-based inference in complex biomedical models.
• The derived methods and procedures are applicable to various statistical and econometric problems with boundary constraints.
• This work facilitates more accurate statistical analysis in fields utilizing constrained parameter spaces.