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Best Parameter Interval for Ridge Estimates by Resampling Method

Abstract

Ridge regression, first proposed by Horel and Kennard [1], is one of the most popular estimation procedures for combating multicollinearity in regression analysis. Although controversial, it is a widely used method to estimate the regression parameters to an ill-conditioned model. Ridge estimates seem to be motivated by a belief that, least square estimates tend to be too large, particularly when there exists any kind of multicollinearity. It gives us a smaller mean square error than OLS estimates for ill- conditioned data. In this paper the ridge procedure has been tried with an interval of shrinkage parameter which has been constructed through bootstrapping approach. Here the intention was to find such an interval for the shrinkage parameter for which the stability of the estimates could be visualized as well as expected change of sign of the parameter values could also be obtained. With this interval another important thing might roughly be obtained that for which value of the ridge parameter, the minimum GCV [2] occurs, could be found. For bootstrapping a random sample from the data matrix has been obtained for each repetition and for the stabilization of the coefficients the method of degrees of freedom trace (DF- trace), which was first proposed by Tripp [3], [14] in his doctoral dissertation, was followed.

Ifte Khyrul Amin Abbas , Pk. M. Motiur Rahman

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