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Research for practical use and new application of resampling method

Research Project

Project/Area Number 11440032
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKYUSHU UNIVERSITY

Principal Investigator

MAESONO Yoshihiro  Faculty of Economics, Kyushu University, Ass. Prof., 大学院・経済学研究院, 助教授 (30173701)

Co-Investigator(Kenkyū-buntansha) KONISHI Tadanori  Graduate School of Mathematics, Kyushu University, Prof., 大学院・数理学研究院, 教授 (40090550)
IWAMOTO Seiichi  Faculty of Economics, Kyushu University, Prof., 大学院・経済学研究院, 教授 (90037284)
YANAGAWA Takashi  Graduate School of Mathematics, Kyushu University, Prof., 大学院・数理学研究院, 教授 (80029488)
HYAKUTAKE Hiroto  Graduate School of Mathematics, Ass. Prof., 大学院・数理学研究院, 助教授 (70181120)
NAKAI Toru  Faculty of Economics, Kyushu University, Professor, 大学院・経済学研究院, 教授 (20145808)
Project Period (FY) 1999 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥6,600,000 (Direct Cost: ¥6,600,000)
Fiscal Year 2001: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2000: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1999: ¥2,500,000 (Direct Cost: ¥2,500,000)
KeywordsNonparametric / Normalizing transformations / resampling / Non-linear model / Markov process / Jackknife / Bootstrap / Information criteria / 動径基底関数 / ファジィ / ボラティリティ / 観測カオス / 二段階法 / 反復ブートストラップ / 判別問題 / 非線形モデリング / ブートストラップ
Research Abstract

In this research project, we have studied problems of resampling method from, a viewpoint of practical use and tried to obtain efficient way of applying the method. We have obtained the following results.
1. In non-parametric statistical inference, we have studied the higher order normalizing transformations which improve convergence rates to normal distribution and obtained new confidence intervals based on the transformations. We have also compared those intervals with bootstrap iteration. Further we propose new bootstrap method which is an approximation of the bootstrap iteration and reduces computation time. 2. For analyzing the time series data, which are strongly non-linear, we propose new estimators of embedded dimension, delay time and Lyapunov exponent. In order to evaluate the variances of these estimators, we apply the bootstrap method and try to improve the estimators. 3. We propose new model criteria, which evaluate the prediction method, and study theoretical properties of the criteria. For analyzing covariance structure, theoretical studies of inferences based on bootstrap method and inferences based on asymptotic expansions have done. 4. Applying the bootstrap method to sequential statistical inferences, we propose a new confidence region of conditional mean, which is based on two-stage procedure and satisfies a size condition. 5. While examining applications of the resampling method to operation research, we propose two new criteria which takes fractional expressions and evaluate expectations of controlled Markov chain. Using recursive method, we also obtain new solutions of optimal and non-optimal problems for deterministic or dynamic systems.
We also develop computer programs which allow us to use the above results practically.

Report

(4 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • Research Products

    (86 results)

All Other

All Publications (86 results)

  • [Publications] MAESONO, Yoshihiko: "On the normal approximations of a studentized symmetric statistic"Mathematica Japonica. 50・3. 433-449 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 前園 宜彦 他: "U-統計量の正規近似の改良とその比較"経済学研究(九州大学経済学会). 66・1. 87-100 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] FUJIOKA, Yumi et al.: "Higher order normalizing transformations for asymptotic U-statistics"Journal of Statistical Planning and Inference. 83. 47-74 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] HALL, Peter et al.: "A weighted-bootstrap approach to bootstrap iteration"Journal of Royal Statistical Society ser. B. 62. 137-144 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] JAYASEKARA, Leslie et al.: "Versatile tests for non-linear data in 2xk tables"Bulletin of Informatics and Cybernetics. 31・2. 179-190 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 北川 源四郎 他: "一般化情報量規準GICとブートストラップ"統計数理. 47・2. 375-394 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] KONISHI, Sadanori: "Statistical model evaluation and information criteria"Multivariate Analysis (Ed. by Subir Ghosh), Marcel Dekker. 369-399 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] NAKAO, Hiroyuki et al.: "A two-stage procedure for fixed-size confidence region of a conditional mean"Bulletin of Informatics and Cybernetics. 31・1. 101-108 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] MAESONO, Yoshihiko: "Nonparametric confidence intervals based on asymptotic expansions"Discussion Paper, Faculty of Economics Kyushu University. 2001-1. 1-25 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] ZHANG, Z-Z.et al.: "On Mantel-Haenszel type estimators in simple nested case-control study"Communication in Statistics-Theory and Methods. 29・11. 2507-2521 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] IWAMOTO, Seiichi: "Nearest route problem"Journal of Mathematical Analysis and Applications. 249・1. 160-178 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] IWAMOTO, Seiichi: "Recursive method in stochastic optimization under compound criteria"Advances in Mathematical Economics. 3. 63-82 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 小西 貞則: "統計的モデリングと情報量規準"応用数理. 10・3. 14-33 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] AOSHIMA, Makoto et al.: "Selection of the best normal population : A new exact solution, asymptotically optimal when k=2"American journal of mathematical and management sciences. 20. 15-26 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] HYAKUTAKE, Hiroto: "Selecting the component with maximal difference of two multinormal means"American journal of mathematical and management sciences. 20. 433-442 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] YANAGAWA, Takashi et al.: "Statistical issues on the determination of the no-observed-adverse-effect levels in toxicology"Environmetrics. 12. 319-325 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] ASTUTI, Erni Tri et al.: "Testing nonlinear trend in proportions under binomial and extra-binomial variabilities"Bulletin of Informatics and Cybernetics. 32・2. 157-168 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] ZHANG, Zhong-Zhan et al.: "Generalized Begun-Reid estimators for multiple hazard rates"Journal of Statistical Planning and Inference. 96. 203-220 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] IWAMOTO, Seiichi: "A class of dual fuzzy dynamic programs"Applied Mathematics and Computation. 120. 91-108 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] ICHIKAWA, Masanori et al.: "Efficient bootstrap tests for the goodness of fit in covariance structure analysis"Behaviormetrika. 28. 103-110 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 安道知寛 他: "動径基底関数ネットワークに基づく非線形回帰モデルとその推定"応用統計学. 30. 19-35 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] NAKAI, Toru: "Learning procedure for a partially observable Markov process and its applications"Discussion Paper, Faculty of Economics Kyushu University. 2001-5. 1-30 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 前園 宜彦: "統計的推測の漸近理論"九州大学出版会. 241 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] MAESONO, Yoshihiko: "On the normal approximations of a studentized symmetric statistic"Mathematica Japonica. Vol.50 No.3. 433-449 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] MAESONO, Yoshihiko et al: "On the improvement of normal approximation for U-statistics and comparisons (in Japanese)"Journal of Political Economy, Kyushu University. Vol.66-1. 87-100 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] FUJIOKA, Yumi et al.: "Higher order normalizing transformations for asymptotic U-statistics"Journal of Statistical Planning and Inference. Vol.83. 47-74 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] HALL, Peter et al.: "A weighted-bootstrap approach to bootstrap iteration"Journal of Royal Statistical Society ser. B. Vol.62. 137-144 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] JAYASEKARA, Leslie et al.: "Versatile tests for non-linear data in 2xk tables"Bulletin of Informatics and Cybernetics. Vol.31-2. 179-190 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] KITAGAWA, Genshiro et al.: "Generalized information criteria GIC and bootstrap (in Japanese)"Toukei Suri. Vol.47-2. 375-394 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] KONISHI, Sadanori: "Statistical model evaluation and information criteria"Multivariate Analysis (Ed. by Subir Ghosh), Marcel Dekker. 369-399 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] NAKAO, Hiroyuki et al.: "A two-stage procedure for fixed-size confidence region of a conditional mean"Bulletin of Informatics and Cybernetics. Vol.31-1. 101-108 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] MAESONO, Yoshihiko: "Nonparametric confidence intervals based on asymptotic expansions"Discussion Paper, Faculty of Economics Kyushu University. No.2001-1. 1-25 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] ZHANG, Z-Z, et al.: "On Mantel-Haenszel type estimators in simple nested case-control study"Communication in Statistics, Theory and Methods. Vol.29-11. 2507-2521 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] IWAMOTO, Seiichi: "Nearest route problem"Journal of Mathematical Analysis and Applications. Vol.249-1. 160-178 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] IWAMOTO, Seiichi: "Recursive method in stochastic optimization under compound criteria"Advances in Mathematical Economics. Vol.3. 63-82 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] KONISHI, Sadanori: "Statistical modeling and information Criteria (in Japanese)"Ouyou Suri. Vol.10-3. 14-33 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] AOSHIMA, Makoto et al.: "Selection of the best normal population : A new exact solution, asymptotically optimal when k=2"American journal of mathematical and management sciences. Vol.20. 15-26 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] HYAKUTAKE, Hiroto: "Selecting the component with maximal difference of two multinormal means"American journal of mathematical and management sciences. Vol.20. 433-442 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] YANAGAWA, Takashi et al.: "Statistical issues on the determination of the no-observed-adverse-effect levels in toxicology"Environmetrics. Vol.12. 319-325 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] ASTUTI, Erni Tri et al.: "Testing nonlinear trend in proportions under binomial and extra-binomial variabilities"Bulletin of Informatics and Cybernetics. Vol.32-2. 157-168 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] ZHANG, Zhong-Zhan et al.: "Generalized Begun-Reid estimators for multiple hazard rates"Journal of Statistical Planning and Inference. Vol.96. 203-220 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] IWAMOTO, Seiichi: "A class of dual fuzzy dynamic programs"Applied Mathematics and Computation. Vol.120. 91-108 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] ICHIKAWA, Masanori et al.: "Efficient bootstrap tests for the goodness of fit in covariance structure analysis"Behaviormetrilka. Vol.28. 103-110 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] ANDO, Tomohiro et al.: "Dokei-kiteikannsu network ni motozuku hisenkei-kaiki to sono suitei (in Japanese)"Japanese Journal of Applied Statistics. Vol.30. 19-35 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] NAKAI, Toru: "Learning procedure for a partially observable Markov process and its applications"Discussion Paper, Faculty of Economics Kyushu University. No.2001-5. 1-30 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] YANAGAWA Takashi et al.: "Statistical issues on the determination of the no-observed-adverse-effect levels in toxicology"Environmetrics. 12. 319-325 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] ASTUTI, Erni Tri et al.: "Testing nonlinear trend in proportions under binomial and extra-binomial variabilities"Bulletin of Informatics and Cybernetics. 32・2. 157-168 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] ZHANG, Zhong-Zhan et al.: "Generalized Begun-Reid estimators for multiple hazard rates"Journal of Statistical Planning and Inference. 96. 203-220 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] ASTUTJ, Erni Tri et al.: "Testing trend for count data with extra-Poisson variability"Biometrics. (掲載予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] IWAMOTO, Seiichi et al.: "On Markov policies for minimax decision processes"Journal of Mathematical Analysis and Applications. 253. 58-78 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] IWAMOTO, Seiichi: "A class of dual fuzzy dynamic programs"Applied Mathematics and Computation. 120. 91-108 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] IWAMOTO, Sejichi: "Recursive method in stochastic optimization under compound criteria"Advances in Mathematical Economic. 3. 63-82 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] FUJITA, Toshiharu et al.: "An optimistic decision-making in fuzzy environment"Applied Mathematics and Computation. 120. 123-137 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] ICHIKAWA, Masanori et al.: "Efficient bootstrap tests for the goodness of fit in covariance structure analysis"Behaviormetrika. 28. 103-110 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 安道知寛 他: "動径基底関数ネットワークに基づく非線形回帰モデルとその推定"応用統計学. 30. 19-35 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] ICHIKAWA, Masanori et al.: "Asymptotic expansions and bootstrap approximations in factor analysis"Journal of Multivariate Analysis. (掲載予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] NAKAI, Toru: "Learning procedure for a partially observable Markov process and its applications"Discussion Paper, Faculty of Economics Kyushu University. No.2001-5. 1-30 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 前園宜彦: "統計的推測の漸近理論"九州大学出版会. 241 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] MAESONO,Yoshihiko: "Nonparametric confidence intervals based on asymptotic expansions"Discussion Paper, Faculty of Economics Kyushu University. No.2001-1. 1-25 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] ZHANG,Z-Z. et al.: "On Mantel-Haenszel type estimators in simple nested case-control study,"Communication in Statistics, Theory and Methods. 29・11. 2507-2521 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] ZHANG,Z-Z. et al.: "Generalized Begun-Reid estimators for multiple hazard rates"Journal of Statistical Planning and Inference. (In Press).

    • Related Report
      2000 Annual Research Report
  • [Publications] YANAGAWA,Takashi: "Statistical issues on the determination of the No-Observed-Adverse-Effect levels in toxicology"Environmetrics. (In Press).

    • Related Report
      2000 Annual Research Report
  • [Publications] IWAMOTO,Seiichi: "Nearest route problem"Journal of Mathematical Analysis and Applications. 249・1. 160-178 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] IWAMOTO,Seiichi: "Recursive method in stochastic optimization under compound criteria"Advances in Mathematical Economics. 3. 63-82 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 小西貞則: "統計的モデリングと情報量規準"応用数理. 10・3. 14-33 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 小西貞則: "統計的モデリングと情報量規準構成の理論-汎関数に基づくアプローチ-"数学. 52・2. 128-141 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] ICHIKAWA,Masanori: "Asymptotic Expansions and Bootstrap Approximations in Factor Analysis"Journal of Multivariate Analysis. (In Press).

    • Related Report
      2000 Annual Research Report
  • [Publications] 宮本正和: "信用リスクのある割引債の離散時間モデルについて"京都大学数理解析研究所講究録「不確実性の下での数理モデルの構築と最適化」. (In Press). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] AOSHIMA,Makoto et al.: "Selection of the best normal population : A new exact solution, asymptotically optimal when k=2"American journal of mathematical and management sciences. 20. 15-26 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] HYAKUTAKE,Hiroto: "Selecting the component with maximal difference of two multinormal means"American journal of mathematical and management sciences. 20(In Press).

    • Related Report
      2000 Annual Research Report
  • [Publications] MAESONO,Yoshihiko: "On the normal approximations of a studentized symmetric statistic."Mathematiga Japonica. 50・3. 433-449 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 前園 宜彦: "U-統計量の正規近似の改良とその比較"経済学研究(九州大学経済学会). 66・1. 87-100 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] MAESONO,Yoshihiko: "Asymptotic representation of ratio statistics its application"The Australian National University,Statistics Research Report. No.SRR006-99. 1-20 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] FUJIOKA,Umi: "Higher order normalizing transformations for asymptotic U-statistics"Journal of Atatistical Planning and Inference. Vol.83. 47-74 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] HALL,Peter: "A weighted-bootstrap approach to bootstrap iteration"Journal of Royal Sratistical Sosieth ser.B. (掲載予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] YANAGAWA,Takashi: "The q-values for controlling the second kind of errors"Bulletin of the International Statistical Institute,ISI99. Book3. 485-486 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] JAYASEKARA,Leslie: "Versatile tests for non-linear date in 2xk tables"Bulletin of Informatics and Cybernetics. 31・2. 179-190 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] IWAMOTO,Seiichi: "Fractional Markov decision processes"京都大学数理解析研究所講究録. 1079. 153-163 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 井元 清哉: "B-スプラインによる非線形回帰モデルと情報量規準"統計数理. 47・2. 359-373 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 北川 源四郎: "一般化情報量基準GICとブートストラップ"統計数理. 47・2. 375-394 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 小西 貞則: "情報量基準構成の理論と応用-最近の発展-"計測と制御. 38・7. 413-419 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] TSUCHIYA,Takahiro: "General saddlepoint approximations to distributions under an elliptical population"Communication in Statistics-Theory and Methods. 28・3&4. 727-754 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] KONISHI,Sadanori: "Statistical model evaluation and information criteria"Multibariate analysis(Ed.by Subir Ghosh),Mercel Dekker. 369-399 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] NAKAI,Toru: "A Generalized MTP2 and a Sequential Stochastic Model on a Partially Observable Markov Process"Proceeding of the First Western Pacific and Third Australia-Japan Workshop on Stochastic Models in Engineering,Technology and Management(Eds.R.J.Wilson et al). 387-396 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] NAKANO,Hiroyuki: "A two-stage procedure for fixed-size confidence region of a conditional mean"Bulletin of Informatics and Cybernetics. 31・1. 101-108 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 前園 宜彦: "概説 確率統計"サイエンス社. 151 (1999)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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