This paper considers inference based on a test statistic that has a limit distribution that is discontinuous in a parameter. The paper shows that subsampling and m out of n bootstrap tests based on such a test statistic often have asymptotic size - defined as the limit of exact size - that is greater than the nominal level of the tests. This is due to a lack of uniformity in the pointwise asymptotics. We determine precisely the asymptotic size of such tests under a general set of high-level conditions that are relatively easy to verify. The results show that the asymptotic size of subsampling and m out of n bootstrap tests is distorted in some examples but not in others.
All Science Journal Classification (ASJC) codes
- Social Sciences (miscellaneous)
- Economics and Econometrics