Subsampling p-values

A construction of p-values for hypothesis tests based on subsampling and the related m out of n bootstrap is introduced. The p-values are based on a modification of the usual subsampling hypothesis tests that involves an appropriate centering of the subsampled or bootstrapped test statistics as in the construction of confidence intervals. This modification makes the hypothesis tests more powerful, and as a consequence provides meaningful p-values. The procedure is shown to apply for both i.i.d. and stationary data satisfying mixing conditions. The new p-values have the desired properties of being asymptotically uniform under the null hypothesis and converging to zero under the alternative.