Robust adaptive Kibria-Lukman estimator for COM-Poisson regression

Abstract

The COM-Poisson regression model is a flexible model for count data that can be overdispersed and underdispersed. However, multicollinearity and contaminated observations can significantly increase estimation variability and reduce the reliability of conventional estimators. This study proposes a Robust Adaptive Kibria–Lukman (RAKL) estimator for COM-Poisson regression using robust and adaptive shrinkage mechanisms. The proposed estimator is a tool that reduces the negative impact of contaminants, multicollinearity and yet provides stable estimation of parameters. A theoretical study of its statistical properties, such as the bias, the covariance matrix and the mean squared error (MSE) matrix, is carried out, and an optimal adaptive biasing parameter is derived to make the estimation more efficient. We perform a large number of Monte Carlo simulations across various sample sizes, predictor dimensions, dispersion levels, and contamination proportions. It is clear from the results that RAKL yields lower MSE, RMSE and MAE values as compared to Robust MLE, Robust Ridge, Robust Liu and Robust Kibria-Lukman estimators in all the cases. A real-data application based on Bike-Sharing data further substantiates the applicability of RAKL in practice. In general, the suggested estimator is a dependable and efficient alternative method for the robust COM-Poisson regression in the presence of multicollinearity and data contamination.