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Researches on the higher order asymptotic theory of statistical inference

统计推断的高阶渐近理论研究

基本信息

批准号：
07454030
负责人：
AKAHIRA Masafumi
金额：
$ 5.06万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

项目摘要

We studied the interval estimation in the theory of higher order asymptotics in statistical inference and an application to a percentage point of the distribution of sample correlation coefficient, and could get useful results in both cases. For discrete distributions it was usually impossible to obtain a non-randomized test or confidence interval with given size, and an actual size was often quite different from the prescribed level. But randomized procedures, which was quite nice in theory, were not easily acceptable to practitioners. So, in this research we constructed a randomized confidence interval from an optimal randomized test, i.e.a uniformly most powerful unbiased test and discussed its approximation using the Edgeworth expansion of the distribution of sufficient statistics. We also investigated that the approximation was accurate in the case of Poisson and binomial distributions.Next, an inference on the correlation coefficient rho is one of the important topics, and until … More now a percentage point of the sample correlation coefficient R has been approximated up to the higher order using the Cornish-Fisher expansion for Fisher's Z-transformation of R.But, unfortunately the approximation way was very complex and a computational treatment must be used. So, in the research we derived a new approximation formula of a percentage point of the distribution of R in a similar way to Akahira (1995) who introduced the approximation formula of a percentage point of the non-central t-distribution. Indeed, we derived the approximation formula using the Cornish-Fisher expansion for the statistic based on a linear combination of a normal random variable and chi-random variables. In numerical calculations, the approximation formula was seen to be that it dominated the normal approximation, the approximation by Fisher's Z-approximation, etc.and gives almost precise values in various cases of alpha and rho even for size 10 of sample.The research was carried out according to plan and the above results were obtained. They were also widely applied to practical problems. Discussions with researchers in related fields were very useful. Less

我们研究了统计推断中高阶渐近理论中的区间估计，以及对样本相关系数分布的一个百分点的应用，在这两种情况下都能得到有用的结果。对于离散分布，通常不可能获得具有给定大小的非随机检验或置信区间，并且实际大小通常与规定水平相差很大。但是随机程序，理论上很好，却不容易被实践者接受。因此，在本研究中，我们从一个最优随机检验，即一致最强大的无偏检验构造了一个随机置信区间，并利用充分统计量分布的Edgeworth展开式讨论了它的近似。我们还研究了在泊松分布和二项分布的情况下，近似是准确的。接下来，对相关系数rho的推断是一个重要的主题，直到现在，一个百分点的样本相关系数R已经近似到高阶，使用的是对R的Fisher的z变换的Cornish-Fisher展开，但不幸的是，近似的方式是非常复杂的，必须使用计算处理。因此，在研究中，我们推导了一个新的R分布的一个百分点的近似公式，类似于Akahira（1995）引入的非中心t分布的一个百分点的近似公式。实际上，我们使用基于正态随机变量和chi随机变量的线性组合的统计量的Cornish-Fisher展开式推导出了近似公式。在数值计算中，近似公式被认为是它支配了正态近似，Fisher的z近似等近似，并且在各种情况下给出了几乎精确的值，甚至对于样本大小为10的alpha和rho。按照计划进行了研究，并取得了上述结果。它们也被广泛应用于实际问题。与相关领域的研究人员的讨论非常有用。少