Computer-intensive statistical methods in multivariate analysis

本研究的目的是探讨多元分析中的计算机密集型统计方法。本研究历时两年多，取得了以下主要成果：1.自举方法在过去的十五年里得到了广泛的研究，并成为构造复杂情况下推理过程的有力工具。关于像Bootstrap这样的计算机密集型方法，已经研究了以下问题：（1）判别分析和模式识别中的预测误差估计方法，（2）Bootstrap在因子分析中最大似然估计的偏差和方差估计中的使用，（3）Bootstrap在模型评估问题中使用的理论和实践方面。2. n中取k：F系统是n个分量的有序序列。通过本课题的研究，得到了以下几点结论：（1）可靠性与 ...更多信息 （2）两状态马尔可夫链中给定长度的成功运行的出现次数。3.研究了满足一定函数方程的极限分布的性质。4.提出了Mantel-Haenszel型检验统计量，用于检验比较二项试验中新处理是否至少与标准处理一样有效。5.研究了当观察到的反应来自正态分布时无明显不良作用水平的确定。研究了几种引入阶数限制的检验方法，提出了一种基于赤池信息量准则的检验方法。6.研究了带一个自由结点的多项式样条函数的逼近问题，证明了满足Braess交替条件的样条函数都是近最优的。7.针对位置、尺度和高阶量的非参数两样本检验问题，提出了新的检验方法。少

The purpose of the research is to investigate the computer intensive statistical methods in multivariate analysis. The followings are the main results obtained through this research project extending over two years.1.The bootstrap methods have been extensively studied for the past fifteen years and become powerful tools for constructing inferential procedures in complex situations. In regard to computerintensive methods like the bootstrap the following problems have been studied ; (1)the methods for predictive error estimation in discriminant analysis and pattern recognition, (2)the use of the bootstrap in the estimation of the biases and variances of maximum likelihood estimates in factor analysis, (3)the theoretical and practical aspects of the use of the bootstrap in model evaluation problems. 2.A consecutive-k-out-of-n : F system is an ordered sequence of n components. The results obtained through the research project are the followings ; (1)the relationship between the reliability … More of the systems and discrete distributions of order k, (2)number of occurrences of success runs of specified length in a two-state Markov chain. 3.Properties of limiting distributions which satisfy certain functional equations were investigated.4.Mantel-Haenszel type test statistics were proposed for testing whether a new treatment is at least as effective as the standard treatment in comparative binomial trials. 5.The determination of the no-observed-adverse-effect level was studied when observed response are from normal distribution. Several tests which incorporate order restriction were examined and a new method based on Akaike's information criterion was proposed. 6.An approximation problem by polynomial spline functions with one free knot was investigated, and it was shown that every spline function satisfying Braess's alternation condition is nearly optimal. 7.New test procedures were proposed for nonparametric two-sample testing problems for location, scale and higher order quantities. Less