Filomat 2017 Volume 31, Issue 10, Pages: 2967-2974
https://doi.org/10.2298/FIL1710967R
Full text ( 255 KB)
A coverage probability of bootstrap-t confidence interval for the variance
Rajić Vesna Ć. (Faculty of Economics, Belgrade)
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.
Keywords: confidence interval, t-statistic, bootstrap, bootstrap-t interval, coverage probability, edgeworth expansion