We investigate the finite-sample coverage properties of confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding. We show that symmetric intervals are the shortest. Among such intervals, the one based on the hard-thresholding estimator is largest whereas the standard interval based on the (unpenalized) maximum likelihood estimator is shortest. In the case where the penalized estimators are tuned to perform consistent model selection, the intervals based on these estimators are larger than the standard one by an order of magnitude. Moreover, a simple asymptotic confidence interval construction in the consistent case is discussed, which also applies to the SCAD estimator.
Keywords: Confidence set; Penalized maximum likelihood estimator; (Adaptive) LASSO, SCAD, soft-thresholding, hard-thresholding
Biography: Institute for Mathematical Stochastics, University of Goettingen