Inequality restricted minimum density power divergence estimation in panel count data

Analysis of panel count data has garnered a considerable amount of attention in the literature, leading to the development of multiple statistical techniques. In inferential analysis, most of the works focus on leveraging estimating equations-based techniques or conventional maximum likelihood estimation. However, the robustness of these methods is largely questionable. In this paper, we present the robust density power divergence estimation for panel count data arising from nonhomogeneous Poisson processes correlated through a latent frailty variable. In order to cope with real-world incidents, it is often desired to impose certain inequality constraints on the parameter space, giving rise to the restricted minimum density power divergence estimator. Being incorporated with inequality constraints, coupled with the inherent complexity of our objective function, standard computational algorithms are inadequate for estimation purposes. To overcome this, we adopt sequential convex programming, which approximates the original problem through a series of subproblems. Further, we study the asymptotic properties of the resultant estimator, making a significant contribution to this work. The proposed method ensures high efficiency in the model estimation while providing reliable inference despite data contamination. Moreover, the density power divergence measure is governed by a tuning parameter γ, which controls the trade-off between robustness and efficiency. To effectively determine the optimal value of γ, this study employs a generalized score-matching technique, marking considerable progress in the data analysis. Simulation studies and real data examples are provided to illustrate the performance of the estimator and to substantiate the theory developed.