Efficient algorithms for computing the non and semi-parametric maximum likelihood estimates with panel count data

Abstract

Nonparametric and semi-parametric analysis of panel count data have recently been active research topics in statistical literature. The maximum likelihood method based on the non-homogeneous Poisson process has been proved an efficient inference procedure for such analysis. However, computing the non- and semi-parametric maximum likelihood estimates (MLEs) can be very intensive numerically and the available methods are not efficient. In this manuscript, we develop an efficient numerical algorithm stemming from the Newton–Raphson method to compute the non- and semi-parametric MLEs for panel count data. Simulation studies are carried out to demonstrate the numerical efficiency of the proposed algorithm compared to the existing methods in the literature.

Keywords:

• quadratic programming
• panel count data
• isotonic regression
• iterative convex minorant algorithm
• Monte-Carlo

Acknowledgement

We thank an anonymous referee for helpful suggestions and comments.