A Coverage Probability of Bootstrap-t Confidence Interval for the Variance

摘要

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 α, 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.