A coverage probability of bootstrap-t confidence interval for the variance

Abstract

We examine one-sided confidence intervals for the population variance, based on the ordinary t-statistics. We derive an unconditional coverage probability of the bootstrap-t interval for unknown variance. For that purpose, we find an Edgeworth expansion of the distribution of t-statistic to an order n-2. We can see that a number of simulation, B, has the influence on coverage probability of the confidence interval for the variance. If B equals sample size then coverage probability and its limit (when B ? ?) disagree at the level O(n-2). If we want that nominal coverage probability of the interval would be equal to ?, then coverage probability and its limit agree to order n-3/2 if B is of larger order than the square root of the sample size. We present a modeling application in insurance property, where the purpose of analysis is to measure variability of a data set.