Abstract
A non-parametric estimator is proposed for the transformation model, where following Box and Cox (1964), we assume that the transform z i = z( y i , λ) of the original data { y i } satisfies a linear model. The estimator is based on the rank correlation of Kendall (1938) and is shown to be strongly consistent. We also find in a Monte Carlo study that the estimator attains greater efficiency in terms of mean squared error than the standard maximum likelihood estimator and the robust estimator of Carroll (1980) when the true error departs from normality. The size of this gain varies with the degree of the departure from normality as well as with the degree of non-linearity of the underlying transformation.
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