Empirical saddlepoint approximations and self-normalized limit theorems

有限总体抽样和重抽样方法，如Bootstrap和随机化方法，是许多应用领域的中心，而M估计是用于在温和条件下提供稳健方法的主要方法；在这两个领域中，都使用了学院化或自归一化的统计学。我们将开发此类统计的渐近方法。用鞍点方法和经验鞍点方法给出在大偏差区域内具有二阶相对精度的方法，得到极限结果和Edgeworth逼近。重点将放在申请所需的弱条件下取得结果。

Finite population sampling and resampling methods such as the bootstrap and randomization methods are central in a number of areas of application and M-estimates are the major method used to give robust methods under mild conditions; in both these areas statistics are used which are Studentized or self-normalized. We will develop asymptotic approaches for such statistics. Saddlepoint and empirical saddlepoint methods will be used to give methods which have second order relative accuracy in large deviation regions and we will obtain limit results and Edgeworth approximations. Emphasis will be on obtaining results under weak conditions necessary for applications.