We develop large deviation results with Cramer's series and the best possible remainder term for bootstrapped U-statistics with non-degenerate bounded kernels. The method of the proof is based on the contraction technique of Keener, Robinson and Weber [R.W. Keener, J. Robinson, N.C. Weber, Tail...

Continuity corrections do not always give a more accurate approximation in the tail area of integer-valued random variables. By studying the relative error, we can compare tail area approximation with and without continuity corrections.

We obtain a saddlepoint approximation for the Studentized mean under stratified random sampling. This is of theoretical interest only, since its calculation requires knowledge of the entire population. We also obtain an empirical saddlepoint approximation based on the stratified sample alone....

We obtain saddlepoint approximations for tail probabilities of the Studentized ratio and regression estimates of the population mean for a simple random sample taken without replacement from a finite population. This is only possible if we know the entire population, so we also obtain empirical...