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

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.