Truncated sequential Monte Carlo test with exact power.

Abstract

Monte Carlo hypothesis testing is extensively used for statistical inference. Surprisingly, despite the many theoretical advances in the field, statistical power performance of Monte Carlo tests remains an open question. Because the last assertion may sound questionable for some, the first goal in this paper is to show that the power performance of truncated Monte Carlo tests is still an unsolved question. The second goal here is to present a solution for this issue, that is, we introduce a truncated sequential Monte Carlo procedure with statistical power arbitrarily close to the power of the theoretical exact test. The most significant contribution of this work is the validity of our method for the general case of any test statistic.