Empirical saddlepoint approximations and self-normalized limit theorems

有限总体抽样和重抽样方法，如自举和随机化方法，在许多应用领域是中心的，m估计是在温和条件下给出鲁棒方法的主要方法；在这两个方面都使用了学生化或自标准化的统计数据。我们将为这类统计发展渐近方法。鞍点法和经验鞍点法将用于给出在大偏差区域具有二阶相对精度的方法，我们将得到极限结果和Edgeworth近似。重点将放在在应用所需的弱条件下获得结果。

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.