Abstract
The use of [1] Box-Cox power transformation in regression analysis is now common; in the last two decades there has been emphasis on diagnostics methods for Box-Cox power transformation, much of which has involved deletion of influential data cases. The pioneer work of [2] studied local influence on constant variance perturbation in the Box-Cox unbiased regression linear mode. Tsai and Wu [3] analyzed local influence method of [2] to assess the effect of the case-weights perturbation on the transformation-power estimator in the Box-Cox unbiased regression linear model. Many authors noted that the influential observations on the biased estimators are different from the unbiased estimators. In this paper I describe a diagnostic method for assessing the local influence on the constant variance perturbation on the transformation in the Box-Cox biased ridge regression linear model. Two real macroeconomic data sets are used to illustrate the methodologies.
Highlights
Deletion diagnostics for assessing the influential cases on the power transformation parameter estimator in the Box-Cox linear unbiased regression model has been intensively studied in the last two and half decades
In this paper I describe a diagnostic method for assessing the local influence on the constant variance perturbation on the transformation in the Box-Cox biased ridge regression linear model
Tsai and Wu [3] applied a case-weights perturbation scheme to obtain an alternative local influence diagnostic that takes into account the perturbation effects of the Jacobian
Summary
Deletion diagnostics for assessing the influential cases on the power transformation parameter estimator in the Box-Cox linear unbiased regression model has been intensively studied in the last two and half decades (see [4,5,6]). Rather than deleting the influential case, [7] proposed a general method for assessing the local influence of minor perturbations of a statistical model. Tsai and Wu [8] analyzed the case-deletion model directly and obtain a more accurate and reliable transformation power estimator in weighted regression model. The aim of this paper is to apply local influence of minor perturbation of constant variance to biased ridge regression Box-Cox power transformation model.
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