liu-type estimator

It is known that when the multicollinearity exists in the gamma regression model, the variance of maximum likelihood estimator is unstable and high. In this article, a new Liu-type estimator based on (r-(k-d)) class estimator in gamma regression model is proposed. The performance of the proposed estimator is studied and comparisons are done with others. Depending on the simulation and real data results in the sense of mean squared error, the proposed estimator is superior to the other estimators.

Modelling of count data has been of extreme interest to researchers. However, in practice, count data is often identified with overdispersion or underdispersion. The Conway Maxwell Poisson regression model (CMPRE) has been proven powerful in modelling count data with a wide range of dispersion. In regression modeling, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator. To address this problem, shrinkage estimators, such as Liu and Liu-type estimators have been consistently verified to be attractive to decrease the effects of multicollinearity. However, these shrinkage estimators are considered biased estimators. In this study, the jackknife approach and its modified version are proposed for modeling count data with CMPRE. These two estimators are proposed to reduce the effects of multicollinearity and the biasedness of using the Liu-type estimator simultaneously. The results of Monte Carlo simulation and real data recommend that the proposed estimators were significant improvement relative to other competitor estimators, in terms of absolute bias and mean squared error with superiority to the modified jackknifed Liu-type estimator.