The m out of n Bootstrap and Goodness of Fit Tests with Double Censored Data

Abstract

This paper considers the use of the m out of n bootstrap (Bickel, Götze, and van Zwet, 1994) in setting critical values for Cramér-von Mises goodness of fit tests with doubly censored data. We show that, as might be expected, the usual n out of n nonparametric bootstrap fails to estimate the null distribution of the test statistic. We show that if the m out of n bootstrap with m → ∞, m = o(n) is used to set the critical value of the test, the proposed testing procedure is asymptotically level α, has the correct asymptotic power function for $$\sqrt n$$ alternatives and is asymptotically consistent.