  In this paper, a semiparametric partially linear model in the spirit of
Robinson (1988) with Box- Cox transformed dependent variable is studied.
Transformation regression models are widely used in applied econometrics to
avoid misspecification. In addition, a partially linear semiparametric model is
an intermediate strategy that tries to balance advantages and disadvantages of
a fully parametric model and nonparametric models. A combination of
transformation and partially linear semiparametric model is, thus, a natural
strategy. The model parameters are estimated by a semiparametric extension of
the so called smooth minimum distance (SmoothMD) approach proposed by Lavergne
and Patilea (2013). SmoothMD is suitable for models defined by conditional
moment conditions and allows the variance of the error terms to depend on the
covariates. In addition, here we allow for infinite-dimension nuisance
parameters. The asymptotic behavior of the new SmoothMD estimator is studied
under general conditions and new inference methods are proposed. A simulation
experiment illustrates the performance of the methods for finite samples.
