Multivariate Statistical Methods for Nonnormal Populations

非正态总体的多元统计方法

基本信息

批准号：
61530018
负责人：
KONISHI Sadanori
金额：
$ 0.77万
依托单位：
The Insitut of Statistical Mathematics
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1986
资助国家：
日本
起止时间：
1986 至 1987
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61530018/
关键词：
Computer Algebra System Edgeworth Expansion Empirical Distribution Function Error Rate in Discriminant Analysis Multivariate Analysis Nonnormal Model 漸近展開統計的汎関数

项目摘要

Intensive investigations have been made concerning the theory and applications of multivariate analysis. Attension has been focused to mustivariate normal distribution.This is mainly due to the fact that the mathematics is intractable for other distributions and many of the procedures developed are shown to have optimal properties in normal model.In practice,However,there often occur the cases in which the normality assumption does not hold.The purpose of this research is to investigate statistical theory and methods in multivariate nonnormal models.The followings are results obtained through the research project.1.The performance of various procedures for selecting variables in linear discriminant analysis was examined both in normal and in nonnormal models.2.A general principle of normalization was constructed based on the rate of convergence to the normal distribution in an Edgeworth expansion.Investigation was made in connection with the problem which arises in deriving higher order Edgeworth expansions.3.The problem of constructing confidence intervals for parameters in multivariate analysis was considered in nonparametric situations.Some procedures were given based on normalizing transformations of estimators. The relationship between Bootstrap confidence intervals and our procedures was considered.4.Higher order asymptotic expansions were obtained for the distributions of the coeffient of variation in nonnormal models and of quadratic forms in normal variables.The hardness of computation was overcome by the use of a computer algebra system,REDUCE-III.5.Asymptotic expansions were derived for the scale mixtures of the normal or of other distributions.Their error bounds were also obtained.6.Some statistics for goodness-of fit tests were constructed based on the martingale term of the empirical distribution function and examined their properties.

人们对多元分析的理论和应用进行了深入的研究。人们的注意力一直集中在必须变量正态分布上。这主要是因为其他分布的数学计算很困难，并且开发的许多程序在正态模型中都显示出具有最优属性。在实践中，然而，经常发生这种情况其中正态假设不成立。本研究的目的是研究多元非正态模型中的统计理论和方法。以下是通过研究项目获得的结果。1.线性判别分析中选择变量的各种程序的性能曾是2.根据埃奇沃斯展开式中正态分布的收敛速度，构建了归一化的一般原理。对推导高阶埃奇沃斯展开式时出现的问题进行了研究。 3.考虑了非参数情况下多元分析中参数置信区间的构建问题，给出了基于估计量归一化变换的程序。考虑了Bootstrap置信区间和我们的程序之间的关系。4.非正态模型中变异系数的分布和正态变量中二次形式的分布得到了高阶渐近展开式。通过使用计算机代数系统，REDUCE-III.5.推导了正态分布或其他分布的尺度混合的渐近展开式。还得到了它们的误差界。6.优度的一些统计拟合检验是基于经验分布函数的鞅项构建的，并检查了它们的属性。