Title: Transformation Models in High-Dimensions,
Abstract: Transformation models are a very important tool for applied statisticians and
econometricians. In many applications, the dependent variable is transformed so
that homogeneity or normal distribution of the error holds. In this paper, we
analyze transformation models in a high-dimensional setting, where the set of
potential covariates is large. We propose an estimator for the transformation
parameter and we show that it is asymptotically normally distributed using an
orthogonalized moment condition where the nuisance functions depend on the
target parameter. In a simulation study, we show that the proposed estimator
works well in small samples. A common practice in labor economics is to
transform wage with the log-function. In this study, we test if this
transformation holds in CPS data from the United States.