Better saddlepoint confidence intervals via bootstrap calibration

Confidence interval construction for parameters of lattice distributions is considered. By using saddlepoint formulas and bootstrap calibration, we obtain relatively short intervals and bounds with $O(n^{-3/2})$ coverage errors, in contrast with $O(n^{-1})$ and $O(n^{-1/2})$ coverage errors for normal theory intervals and bounds when the population distribution is absolutely continuous. Closed form solutions are also provided for the cases of binomial and Poisson distributions. The method is illustrated by some simulation results.