Project/Area Number  05680258 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
Statistical science

Research Institution  KYUSHU UNIVERSITY 
Principal Investigator 
KONISHI Sadanori Kyushu Univ. : Graduate school of Math. : Professor, 大学院・数理学研究科, 教授 (40090550)

CoInvestigator(Kenkyūbuntansha) 
HIRANO Katuomi Institute of Statistical Math. : Professor, 統計基礎研究系, 教授 (30000186)
SHIMIZU Ryoichi Institute of Statistical Math. : Director General, 所長 (10000192)
KAWASAKI Hidefumi Kyushu Univ. : Graduate School of Math. : Associ.Prof., 大学院・数理学研究科, 助教授 (90161306)
FUEDA Kaoru Kyushu Univ. : Graduate School of Math. : Assis.Prof., 大学院・数理学研究科, 助手 (50253399)
YANAGAWA Takashi Kyushu Univ. : Graduate School of Math. : Professor, 大学院・数理学研究科, 教授 (80029488)

Project Fiscal Year 
1993 – 1994

Project Status 
Completed(Fiscal Year 1994)

Budget Amount *help 
¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 1994 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1993 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Bootstrap / Information criteria / Reliability of the systems / Categorical data / Spline functions / Reduction of dimensionality / Model evaluation / Comparative clinical trials / ブートストラップ / 情報量規準 / システムの信頼性 / カテゴリカルデータ / スプライン関数 / 次元縮少 / モデル評価 / 比較臨床試験 / 情報量基準 / ブートストラップ法 / 構造分析 / 変化点問題 / ノンパラメトリック検定 / 離散多変量データ / 判別分析 / 因子分析 / 統計モデル / 予測誤差 / 離散分布論 
Research Abstract 
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 consecutivekoutofn : 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
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of the systems and discrete distributions of order k, (2)number of occurrences of success runs of specified length in a twostate Markov chain. 3.Properties of limiting distributions which satisfy certain functional equations were investigated.4.MantelHaenszel 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 noobservedadverseeffect 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 twosample testing problems for location, scale and higher order quantities. Less
