Nonparametric Predictive Inference Bootstrap with Application to Reproducibility of the Two-Sample Kolmogorov–Smirnov Test

Abstract

This paper introduces a new bootstrap method based on the nonparametric predictive inference (NPI) approach to statistics.NPI is a frequentist statistics framework which explicitly focuses on prediction of future observations. The NPI framework enables a bootstrap method (NPI-B) to be introduced which, different to Efron’s classical bootstrap (Ef-B), is aimed at prediction of future observations instead of estimation of population characteristics.A brief initial comparison of NPI-B and Ef-B is presented. The main reason for introducing NPI-B here is for its application to NPI for reproducibility of statistical tests, which is illustrated for the two-sample Kolmogorov–Smirnov test.