Generalized ridge regresyon by using deformed logarithms

Ridge regression is an alternative approach in regression analysis when there is multicollinearity problem between independent variables. The aim of this study is to define M-estimators which is a generalization of the likelihood estimators by using deformed logarithms and to perform ridge regression analysis with M-estimators based on deformed logarithms. In this way, both multicollinearity problem will be overcome and robust estimations will be obtained.. In order to demonstrate the effectiveness and applicability of the proposed method, two applications was performed on the real data sets. The importance of ridge parameter was determined in ridge regression using M-estimation method based on deformed logarithms and comparisons of ridge Huber M-estimation and Student t distribution regression parameters with maximum likelihood estimators were made.