On the choice of the ridge parameter: a generalized maximum Tsallis entropy approach.

In multiple Regression Model the absence of multicollinearity is essential. The presence of multicollinearity is often caused by including too many (highly correlated) regressors and in this case, the estimates tend to be less precise. For this reason, varies methods have been introduced to solve these problems caused by the existence of multicollinearity. In this paper, a new method to estimate the ridge parameter, based on the ridge trace and an analytical method borrowed from Generalized Maximum Tsallis Entropy, is presented and we call that the Ridge GMET2 estimator. The performance of the new estimator is illustrated through a Monte Carlo simulation study. We compared the Ridge GMET2, Ridge GME and OLS estimators. Mean square error of Ridge GMET2 estimates, is less than corresponding for Ridge-GME and OLS estimates. In some case also, the value of the Ridge-GME and Ridge-GMET2 estimators are nearer, since Tsallis entropy does not depend on the logarithm unlike, the Shannon entropy, so that it is a substantial point that we prefer the Ridge-GMET2 estimator. [ABSTRACT FROM AUTHOR]