Computer-intensive statistical methods in multivariate analysis

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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