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统计方法。以下是本课题历时两年多的主要研究成果。自举方法在过去的15年中得到了广泛的研究，并成为在复杂情况下构建推理过程的有力工具。对于像bootstrap这样的计算机密集型方法，研究了以下问题；(1)判别分析和模式识别中预测误差估计的方法；(2)在因子分析中最大似然估计的偏差和方差估计中使用自举法；(3)在模型评估问题中使用自举法的理论和实践方面。2.一个连续的-k （n: F）系统是一个有n个分量的有序序列。通过研究项目获得的结果如下：(1)系统的可靠性与k阶离散分布之间的关系；(2)两态马尔可夫链中指定长度的成功运行的出现次数。3.研究了满足某些泛函方程的极限分布的性质。在比较二项试验中，提出了Mantel-Haenszel型检验统计量，用于检验新治疗是否至少与标准治疗一样有效。5.当观察到的反应服从正态分布时，研究了未观察到的不良反应水平的确定。研究了几种包含订单限制的测试方法，提出了基于赤池信息准则的新方法。6.研究了带一个自由结的多项式样条函数逼近问题，证明了满足bress交替条件的每一个样条函数都是近最优的。7.针对位置、规模和高阶量的非参数双样本测试问题，提出了新的测试方法。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