  In this paper, we study the linear transformation model in the most general
setup. This model includes many important and popular models in statistics and
econometrics as special cases. Although it has been studied for many years, the
methods in the literature are based on kernel-smoothing techniques or make use
of only the ranks of the responses in the estimation of the parametric
components. The former approach needs a tuning parameter, which is not easily
optimally specified in practice; and the latter is computationally expensive
and may not make full use of the information in the data. In this paper, we
propose two methods: a pairwise rank likelihood method and a
score-function-based method based on this pairwise rank likelihood. We also
explore the theoretical properties of the proposed estimators. Via extensive
numerical studies, we demonstrate that our methods are appealing in that the
estimators are not only robust to the distribution of the random errors but
also lead to mean square errors that are in many cases comparable to or smaller
than those of existing methods.
