Simultaneous directional inference
同时方向性推断
We consider the problem of inference on the signs of $n>1$ parameters. We aim to provide $1-α$ post-hoc confidence bounds on the number of positive and negative (or non-positive) parameters. The guarantee is simultaneous, for all subsets of parameters. Our 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…