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 ” 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 when the number of parameters goes to infinity. Anew consistent estimator of order 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.
Highlights
The Box-Cox transformation model (BC model) [1] is widely used in empirical studies
This paper considers the asymptotic efficiency of the maximum likelihood estimator (MLE) for the Box-Cox transformation model with heteroscedastic disturbances
The maximum likelihood estimator (MLE), which maximizes the likelihood function under the normality assumption (BC MLE), can be asymptotically efficient if the “small σ ” condition described by Bickel and Doksum [4] is satisfied
Summary
The Box-Cox transformation model (BC model) [1] is widely used in empirical studies. For details on this model, see Hossain [2] and Sakia [3]. Nawata 836 of stay (LOS) in Japanese hospitals using the BC model They found that the variances among hospitals were often very different among hospitals even after the transformation. It is necessary for us to consider the asymptotic properties of estimators when the number of groups (hospitals) goes to infinity. This paper considers the estimation of the Box-Cox transformation model with heteroscedastic disturbances when the number of groups that increases to infinity. In such cases, the conventional maximum likelihood method yields only an estimator whose rate of convergence is slower than ordinal order of 1 n even if the “small σ ” condition is satisfied in all groups. A new estimation method that can handle these problems is proposed
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