Inequality Constrained Minimum Density Power Divergence Estimation in Panel Count Data

The analysis of panel count data has garnered considerable attention in the literature, leading to the development of multiple statistical techniques. In inferential analysis, most works focus on leveraging estimating equation-based techniques or conventional maximum likelihood estimation. However, the robustness of these methods is largely questionable. In this paper, we present a robust density power divergence estimation method for panel count data arising from non-homogeneous Poisson processes correlated through a latent frailty variable. To cope with real-world incidents, it is often desirable to impose certain inequality constraints on the parameter space, leading to the constrained minimum density power divergence estimator. Being incorporated with inequality restrictions, 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 $\gamma$, which controls the trade-off between robustness and efficiency. To effectively determine the optimal value of $\gamma$, 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.