Theory and Algorithms Commons^™

Computing Highly Accurate Or Exact P-Values Using Importance Sampling, Chris Lloyd

Chris J. Lloyd

Especially for discrete data, standard first order P-values can suffer from poor accuracy, even for quite large sample sizes. Moreover, different test statistics can give practically different results. There are several approaches to computing P-values which do not suffer these defects, such as parametric bootstrap P-values or the partially maximised P-values of Berger and Boos (1994).

Both these methods require computing the exact tail probability of the approximate P-value as a function of the nuisance parameter/s, known as the significance profile. For most practical problems, this is not computationally feasible. I develop an importance sampling approach to this problem. A …