Robust estimation with discrete explanatory variables

The least squares estimator is quite sensitive to data contamination and model misspecification. This sensitivity is addressed by the theory of robust statistics which builds upon parametric specification, but provides methodology for designing misspecification-proof estimators by allowing for various ".departures" of subsets of the data. Unfortunately, most of highly robust estimators developed within robust statistics cannot be easily applied to models containing binary and categorical explanatory variables. Therefore, we design a robust estimator based on least trimmed squares that can be used for any linear regression model no matter what kind, of explanatory variables the model contains. Additionally, we propose an adaptive procedure that maximizes the efficiency of the proposed estimator for a given data set while preserving its robustness.