Asymptotic Efficiency of the Maximum Likelihood Estimator for the Box-Cox Transformation Model with Heteroscedastic Disturbances

Abstract

This paper considers the asymptotic efficiency of the maximum likelihood estimator (MLE) for the Box-Cox transformation model with heteroscedastic disturbances. The MLE under the normality assumption (BC MLE) is a consistent and asymptotically efficient estimator if the "small σ " condition is satisfied and the number of parameters is finite. However, the BC MLE cannot be asymptotically efficient and its rate of convergence is slower than ordinal order 1 n when the number of parameters goes to infinity. Anew consistent estimator of order 1 n is proposed. One important implication of this study is that estimation methods should be carefully chosen when the model contains many parameters in actual empirical studies.