Transforming variables to central normality

Many real data sets contain 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 an automatic preprocessing technique that is robust against such outliers, which transforms the data to central normality. It compares favorably to existing techniques in an extensive simulation study and on real data.