Nonparametric Estimation of the Transformation in the Transform-Both-Sides Regression Model

Abstract

The transform-both-sides (TBS) regression model developed by Carroll and Ruppert is applicable when the relationship between the median response and the independent variables has been identified. Several different families of transformations, such as the Box-Cox power family, have been considered in the parametric approach to this model. In this article, we propose a nonparametric estimator of the transformation in the TBS model allowing general smooth monotonic transformations. Asymptotic properties of this estimator are discussed.