Post-selection Inference

2016 • 115 pages • EN

Written by Alexandra Bolotskikh

Researchers are often interested in making inference on one or a few "best" treatment out of p given treatments. This problem is referred to as post-selection inference. Substantial research has been done on constructing point estimates and confidence sets for a multivariate normal mean vector, but there are very few works on inference after selection. Often, out of all available estimates, the ones that are minimax and/or admissible are preferred. It was shown by Sackrowitz & Samuel-Cahn (1986) that X1, the first order statistic, is minimax for estimating the selected mean for p [LESS-THAN OR EQUAL TO] 3, but it is not minimax for p> 3, but the question whether it is admissible was still open. In Chapter 1, following the arguments of Berger (1976a) and Maruyama (2009) we prove that X1 is admissible for p