Statistics Seminar: Robinson -- Asymptotic Approximations in Sampling and Resampling

The ideas of sampling with and without replacement connect each of the areas of finite
population samples, permutation tests, rank tests and bootstrap methods.  Normal and
Edgeworth approximations, Cramer large deviation results and related saddlepoint
approximations have been obtained in one and two sample cases, and some results on
Studentized statistics, k-sample and multivariate cases have been obtained quite
recently.  In the case of the bootstrap, asymptotic methods have been used to give
theoretical results on their accuracy.  I will survey of some of the main asymptotic
methods and indicate in more detail some relatively recent results, on approximations
for Studentized and multivariate statistics.