TITLE:
Asymptotic Efficiency of the Maximum Likelihood Estimator for the Box-Cox Transformation Model with Heteroscedastic Disturbances
AUTHORS:
Kazumitsu Nawata
KEYWORDS:
Maximum Likelihood Estimator (MLE), Asymptotic Efficiency, Box-Cox Transformation Model, Heteroscedasticity
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.5,
October
21,
2016
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.