Penalized nonparametric likelihood-based inference for current status data model

Abstract

Deriving the limiting distribution of a nonparametric estimate is rather challenging but of fundamental importance to statistical inference. For the current status data, we study a penalized nonparametric likelihood-based estimator for an unknown cumulative hazard function, and establish the pointwise asymptotic normality of the resulting nonparametric esti-mate. We also propose the penalized likelihood ratio tests for local and global hypotheses, derive their limiting distributions, and study the opti-mality of the global test. Simulation studies show that the proposed method works well compared to the classical likelihood ratio test.