Modified jackknife ridge estimator for the Conway-Maxwell-Poisson model

Abstract

Recently, research papers have shown a strong interest in modeling count data. The over-dispersion or under-dispersion are frequently seen in the count data. The count data modeling with a broad range of dispersion has been successfully accomplished using the Conway-Maxwell-Poisson regression (COMP) model. The multicollinearity issue is known to have a detrimental impact on the maximum likelihood estimator's variance. To solve this issue, biased estimators as a ridge estimator have repeatedly shown to be an appealing way to minimize the effects of multicollinearity. In this paper, we suggested the jackknife ridge estimator (JCOMPRE) and the modified version of the jackknife ridge estimator (MJCOMPRE) for the COMP model. The proposed estimators (JCOMPRE and MJCOMPRE) are reducing the effects of the multicollinearity and the biasedness of the ridge estimator at the same time. According to the findings of the Monte Carlo simulation study and real-life applications, the proposed estimators have a minimum bias and a minimum mean squared error. This means that the proposed estimators are more efficient than the maximal likelihood estimator and the ridge estimator.