B0613
Title: Simultaneous directional inference
Authors: Ruth Heller - Tel-Aviv University (Israel) [presenting]
Aldo Solari - University of Milano-Bicocca (Italy)
Abstract: The problem of inference on the signs of $n>1$ parameters is considered. The aim is to provide $1-\alpha$ post-hoc confidence bounds on the number of positive and negative (or non-positive) parameters. The guarantee is simultaneous, for all subsets of parameters. Thus, for any subset of parameters, lower confidence bounds are provided on their signs, as well as directional decisions on individual parameters. The suggestion is as follows: start by using the data to select the direction of the hypothesis test for each parameter; then, adjust the $p$-values of the one-sided hypotheses for the selection, and use the adjusted $p$-values for simultaneous inference on the selected $n$ one-sided hypotheses. The adjustment is straightforward assuming that the $p$-values of one-sided hypotheses are conditionally valid and mutually independent. The bounds provided are tighter (often by a great margin) than existing alternatives, and they can be obtained by at most a polynomial time. The usefulness of the simultaneous post-hoc bounds is demonstrated in several applications.
