Edgeworth and Saddle-Point Approximations with Statistical Applications

Summary A simple exposition is given of Edgeworth and saddle-point approximations for some univariate, multivariate and conditional distributions. The application of these approximations to some problems of conditional statistical inference within the exponential family is illustrated. Examples connected with the time-dependent Poisson process, the von Mises distribution and with bioassay are among those studied in a little detail. Some general results are derived about conditional likelihoods and about the distribution of the maximum likelihood ratio test statistic. An appendix discusses regularity conditions.