  Many real data sets contain numerical features (variables) whose distribution
is far from normal (gaussian). Instead, their distribution is often skewed. In
order to handle such data it is customary to preprocess the variables to make
them more normal. The Box-Cox and Yeo-Johnson transformations are well-known
tools for this. However, the standard maximum likelihood estimator of their
transformation parameter is highly sensitive to outliers, and will often try to
move outliers inward at the expense of the normality of the central part of the
data. We propose a modification of these transformations as well as an
estimator of the transformation parameter that is robust to outliers, so the
transformed data can be approximately normal in the center and a few outliers
may deviate from it. It compares favorably to existing techniques in an
extensive simulation study and on real data.
