Modified ridge parameter estimators for log-gamma model: Monte Carlo evidence with a graphical investigation

Abstract

In ordinary ridge regression, the estimation of the ridge parameter is a significant topic. This article generalizes some different methods for estimating the ridge parameter by considering the work of Kibria (2003), Khalaf and Shukur (2005), Alkhamisi, Khalaf, and Shukur (2006), Alkhamisi and Shukur (2008) and Muniz et al. (2012) in generalized linear models. The superiority of these estimators are assessed by the estimated mean squared error via Monte Carlo simulation study and real data set where the response follows gamma distribution with log link function. In this simulation study, it is chosen to vary the degree of correlation, the sample size, the number of explanatory variables and the different shape parameter for gamma response.

Keywords:

• Ridge parameter estimator
• Log-gamma model
• Generalized linear models
• Mean squared error