A new gamma regression estimate of female body fat percentage: advanced statistical modeling

Abstract

In this paper, a new gamma two-step shrinkage (GTSS) estimator is proposed for the gamma regression model to address the issue of multicollinearity. We derived the mean squared error (MSE) for the proposed estimator and defined the necessary and sufficient conditions for its superiority over five existing estimators. A comprehensive comparison is conducted between the proposed GTSS estimator and traditional maximum likelihood (ML) estimator, Liu estimator, and other conventional estimators, using a matrix mean squared error criterion. The results from the Monte Carlo simulation demonstrate the advantages of the proposed GTSS estimator under various conditions, particularly in the presence of severe multicollinearity. Additionally, we analyzed a real-world dataset on body fat to illustrate the practical relevance and effectiveness of our new estimator, showing significant reductions in the estimated mean squared error. As a result, the precision of the estimated parameters improves substantially, fulfilling one of the primary objectives for practitioners in this field.