Empirical saddlepoint approximations and self-normalized limit theorems

经验鞍点近似和自归一化极限定理

• 批准号: DP0451722
• 负责人: Em/Prof John Robinson
• 金额: $ 15.67万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2004
• 资助国家: 澳大利亚
• 起止时间: 2004-02-01 至 2007-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0451722
• 关键词: Empirical; saddlepoint; approximations; self; normalized

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.

有限的人口抽样和restaurant方法，如自助法和随机化方法是中央在一些领域的应用和M-估计是主要的方法，用于提供强大的方法在温和的条件下，在这两个领域的统计使用的是学生化或自我规范化。我们将发展这种统计的渐近方法。鞍点和经验鞍点方法将被用来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。重点将是在弱条件下获得应用所需的结果。