Estimation for the Box-Cox Transformation Model Without Assuming Parametric Error Distribution
Box and Cox proposed a power transformation for the response variable that yields a linear regression model with normal error and constant variance. Inference procedures for the regression coefficients and transformation parameter under this model setting have been studied extensively. In this article we propose a simple semiparametric estimation method for the Box–Cox transformation model with no specific parametric assumption on the distribution of the error term. The resulting estimators are strongly consistent and asymptotically normal. Their covariance matrix can be estimated through a novel resampling method without involving nonparametric function estimates of the underlying unknown density function for the error term. The new proposal is illustrated with a well-known dataset in the literature of transformation, and its efficiency and robustness are closely examined through numerical studies.