Two new data-dependent choices of m when applying the m-out-of-n bootstrap to hypothesis testing

Abstract

The traditional non-parametric bootstrap (referred to as the n-out-of-n bootstrap) is a widely applicable and powerful tool for statistical inference, but in important situations it can fail. It is well known that by using a bootstrap sample of size m, different from n, the resulting m-out-of-n bootstrap provides a method for rectifying the traditional bootstrap inconsistency. Moreover, recent studies have shown that interesting cases exist where it is better to use the m-out-of-n bootstrap in spite of the fact that the n-out-of-n bootstrap works. In this paper, we discuss another case by considering its application to hypothesis testing. Two new data-based choices of m are proposed in this set-up. The results of simulation studies are presented to provide empirical comparisons between the performance of the traditional bootstrap and the m-out-of-n bootstrap, based on the two data-dependent choices of m, as well as on an existing method in the literature for choosing m. These results show that the m-out-of-n bootstrap, based on our choice of m, generally outperforms the traditional bootstrap procedure as well as the procedure based on the choice of m proposed in the literature.