High-dimensional variable screening and bias in subsequent inference, with an empirical comparison

We review variable selection and variable screening in high-dimensional linear models. Thereby, a major focus is an empirical comparison of various estimation methods with respect to true and false positive selection rates based on 128 different sparse scenarios from semi-real data (real data covariables but synthetic regression coefficients and noise). Furthermore, we present some theoretical bounds for the bias in subsequent least squares estimation, using the selected variables from the first stage, which have direct implications for construction of p-values for regression coefficients.