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The Foundation of Mathematical Statistics on Quantum Inference and Its Applications

Research Project

Project/Area Number 14204006
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionUniversity of Tsukuba

Principal Investigator

AKAHIRA Masafumi  University of Tsukuba, Graduate School of Pure and Applied Sciences, Professor, 大学院・数理物質科学研究科, 教授 (70017424)

Co-Investigator(Kenkyū-buntansha) AOSHIMA Makoto  University of Tsukuba, Graduate School of Pure and Applied Sciences, Associate Professor, 大学院・数理物質科学研究科, 助教授 (90246679)
HAYASHI Masato  University of Tokyo, Graduate School of Information Science and Technology, Associate Professor, 大学院・情報理工学研究科, 助教授 (40342836)
YAMATO Hajime  Kagoshima University, Faculty of Science, Professor, 理学部, 教授 (90041227)
KAGEYAMA Sanpei  Hiroshima University, Faculty of Education, Professor, 大学院・教育研究科, 教授 (70033892)
MAESONO Yoshihiko  Kyushu University, Faculty of Economics, Professor, 大学院・経済学研究院, 教授 (30173701)
高木 祥司  大阪府立大学, 大学院・工学研究科, 助教授 (00231390)
白倉 暉弘  神戸大学, 発達科学部, 教授 (30033913)
今井 浩  東京大学, 大学院情報理工学研究科, 教授 (80183010)
吉田 朋広  東京大学, 大学院・数理科学研究科, 教授 (90210707)
近藤 正男  鹿児島大学, 理学部, 教授 (70117505)
松本 啓史  国立情報学研究所, 情報学基礎, 助教授 (60272390)
宇野 力  秋田大学, 教育文化学部, 助教授 (20282155)
狩野 裕  大阪大学, 基礎工学研究科, 教授 (20201436)
白石 高章  横浜市立大学, 理学部, 教授 (50143160)
櫻井 明夫  京都産業大学, 理学部, 教授 (50013496)
高田 佳和  熊本大学, 工学部, 教授 (70114098)
栗木 哲  統計数理研究所, 助教授 (90195545)
柿沢 佳秀  北海道大学, 経済学部, 助教授 (30281778)
磯貝 英一  新潟大学, 理学部, 教授 (40108014)
Project Period (FY) 2002 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥46,410,000 (Direct Cost: ¥35,700,000、Indirect Cost: ¥10,710,000)
Fiscal Year 2005: ¥12,480,000 (Direct Cost: ¥9,600,000、Indirect Cost: ¥2,880,000)
Fiscal Year 2004: ¥11,050,000 (Direct Cost: ¥8,500,000、Indirect Cost: ¥2,550,000)
Fiscal Year 2003: ¥11,050,000 (Direct Cost: ¥8,500,000、Indirect Cost: ¥2,550,000)
Fiscal Year 2002: ¥11,830,000 (Direct Cost: ¥9,100,000、Indirect Cost: ¥2,730,000)
KeywordsQuantum estimation / Quantum test / Quantum information geometry / Sequential analysis / Sequential estimation / Combinatorial theory / Experimental design / Quantum mechanics / ロバスト法 / 最尤法 / 多変量解析 / 量子統計 / 確率過程 / 情報不等式 / 因子分析 / 統計的推定 / 統計的検定 / 分割表 / 数理ファイナンス / 量子情報 / 量子エンタングルメント / 回帰モデル / 混合モデル / 情報量 / 統計的モデル / 統計量 / デザイン理論 / 逐次解析 / バイオスタティスティクス / ゲノムデータ解析
Research Abstract

The statistical investigation on various themes was done as follows. (1) Involving a relationship between statistical models and statistics, the properties of the models were discussed and some interesting results on the behavior of various statistics are obtained. (2) In the theory of statistics to finance, time series and their applications, statistical procedures were shown to be asymptotically useful. (3) In the experimental design and its related area, the mathematical structure is clarified by combinatorial procedures, and results intended to apply to practical problems were obtained. (4) In statistical sequential inference, some sequential procedures were proposed, and their properties were discussed in details. The asymptotic efficiencies were shown. (5) The construction of mathematically fundamental theory of biostatistics is tried, and statistically inferential procedures are shown to play an important role. In particular, bioassay test, score test etc. were shown to be usefu … More l. (6) The relationship between non-locality in quantum mechanics and statistical inference is clarified, and inferential procedures is also shown to be efficient in quantum estimation and quantum test. Further, it is recognized to play an important role as the theoretical base of concrete physical phenomena. (7) In statistical inference, on the lower bound for tail probabilites of consistent estimators, the first and second order asymptotic efficiencies are investigated from a different viewpoint from conventional Bahadur efficiency. And in order to unify both of non-parametric and parametric tests, the mathematical setup was done, new test statistics based on estimators of spectral density matrics were proposed, and their asymptotic properties are derived. (8) Under a family of non-parametric quantum states, state estimation, prediction of quantum state, quantum information geometry and discrimination problem on quantum states are trated, and new interesting results were obtained. Many symposium on the above were held and active discussion and mutual exchange of information were also done. Their results were summarized as a volume. Less

Report

(5 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (40 results)

All 2006 2005 2004 2003 Other

All Journal Article (24 results) Book (3 results) Publications (13 results)

  • [Journal Article] 統計的推定の高次漸近理論の構造2006

    • Author(s)
      赤平昌文
    • Journal Title

      数学(日本数学会和文誌) 58-1

      Pages: 1-20

    • NAID

      10017554608

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Non-validity of affine α-resolvability in regular group derisible designs2006

    • Author(s)
      S.Kageyama
    • Journal Title

      J. Statist. Plann. Inference (掲載予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The structure of higher order asymptotic theory of statistical estimation. (In Japanese)2006

    • Author(s)
      Akahira, M.
    • Journal Title

      Sugaku 58(1)

      Pages: 1-20

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Non-validity of affine α-resolvability in regular group divisible designs.2006

    • Author(s)
      Kageyama, S.
    • Journal Title

      J.Statist.Plann.Inference (to appear.)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 統計的推定の高次漸近理論の構造2006

    • Author(s)
      赤平昌文
    • Journal Title

      数学(日本数学会 和文誌) 58-1

      Pages: 1-20

    • NAID

      10017554608

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Bhattacharyya型情報不等式について2006

    • Author(s)
      田中 秀和
    • Journal Title

      数学(日本数学会 和文誌) 58-1

      Pages: 21-39

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Large-deviation efficiency of first and second order2005

    • Author(s)
      M.Akahira
    • Journal Title

      Student 5-1(印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic representations of ratis statistics and their mean squared errors2005

    • Author(s)
      Y.Maesono
    • Journal Title

      J. Japan Statist. Soc. 35-1

      Pages: 73-97

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Large-deviation efficiency of first and second order.2005

    • Author(s)
      Akahira, M.
    • Journal Title

      Student 5(1)(In press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic representations of ratio statistics and their mean squared errors.2005

    • Author(s)
      Maesono, Y.
    • Journal Title

      Journal of the Japan Statistical Society 35

      Pages: 73-97

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Large-deviation efficiency of first and second order2005

    • Author(s)
      Akahira, M.
    • Journal Title

      Student 5-3(印刷中)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Asymptotic representation of ratio statistics and their mean squared errors2005

    • Author(s)
      Maesono, Y.
    • Journal Title

      J.Japan Statist.Soc. 35-1

      Pages: 73-97

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Behadur exact slopes of some tests for spectral density2005

    • Author(s)
      Kakizawa, Y.
    • Journal Title

      Journal of Nonparametric Statistics 17-6

      Pages: 745-764

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 時系列に対する判別解析2005

    • Author(s)
      谷口 正信
    • Journal Title

      日本統計学会誌 35-1

      Pages: 71-79

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Sequential interval estimation of location parameter with the fixed width in the uniform distribution2005

    • Author(s)
      Akahira, M., Koike, K.
    • Journal Title

      Sequential Analysis 24-1

      Pages: 1-13

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Asymptotic second-order efficiency for multivariate two-stage estimation of a linear function of normal mean rectors2004

    • Author(s)
      M.Aoshima, Y.Takada
    • Journal Title

      Sequential Analysis 23-3

      Pages: 333-353

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic second-order efficiency for multivariate two-stage estimation of a linear function of normal mean vectors.2004

    • Author(s)
      Aoshima, M., Takada, Y.
    • Journal Title

      Sequential Analysis 23(3)

      Pages: 333-353

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Large-deviation efficiency of first and second order2004

    • Author(s)
      Akahira, M.
    • Journal Title

      Mathematical Research Note, Inst. of Math., Univ. of Tsukuba 2004-006

      Pages: 1-10

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On a family of distributions attaining the Bhattacharyya bound2004

    • Author(s)
      田中秀和
    • Journal Title

      数理解析研究所講究録 1380

      Pages: 63-79

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 拡散過程に対する判別関数の漸近展開2004

    • Author(s)
      坂本雄二
    • Journal Title

      数理解析研究所講究録 1380

      Pages: 140-151

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Two-stage multiple comparisons with components of a linear function of mean vectors2004

    • Author(s)
      Kushida, T., Aoshima, M.
    • Journal Title

      数理解析研究所講究録 1380

      Pages: 33-51

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Testing Hypothesis for quantum systems2004

    • Author(s)
      Tsuda, Y., Hayashi, M, Matsumoto, K.
    • Journal Title

      数理解析研究所講究録 1380

      Pages: 98-105

    • Related Report
      2004 Annual Research Report
  • [Journal Article] General formulas for capacity of classical-quantum channels2003

    • Author(s)
      M.Hayashi, H.Nagaoka
    • Journal Title

      IEEE Transactions on Information Theory 49-7

      Pages: 1753-1768

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] General formulas for capacity of classical-quantum channels.2003

    • Author(s)
      Hayashi, M., Nagaoka, H.
    • Journal Title

      IEEE Transactions on Information Theory 49, No.7

      Pages: 1753-1768

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] 特異モデルの統計学2004

    • Author(s)
      福水健次, 栗木哲, 竹内啓, 赤平昌文
    • Publisher
      岩波書店
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] Statistics of Singular Models. (In Japanese)2004

    • Author(s)
      Fukumizu, K., Kuriki, S., Takeuchi, K., Akahira, M.
    • Publisher
      Iwanami-shoten, Tokyo
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] 特異モデルの統計学2004

    • Author(s)
      福永健次, 栗本 哲, 竹内 啓, 赤平 昌文
    • Total Pages
      274
    • Publisher
      岩波書店
    • Related Report
      2004 Annual Research Report
  • [Publications] Akahira, M., Takeuchi, K.: "The information inequality in Sequential estimation for the uniform Case"Sequential Analysis. 22-3. 223-232 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Akahira, M., Ohyauchi, N.: "An information inequality for the Bayes risk applicable to non-regular cases"数理解析研究所講究録. 1334. 183-191 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Akahira, M., Takeuchi, K.: "On the loss of power of a test based on simulation"数理解析研究所講究録. 1334. 192-195 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hida, E., Akahira, M.: "An approcimation to the generalyed hyporgeomatric distribution"Statistical Papers. 44-4. 483-497 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Tanaka, H., Akahira, M.: "On a family of distributions attaining the Bhattacharyya bound"Ann.Inst.Statist.Math.. 55-2. 309-317 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Aoshima, M. et al.: "Monotone Bartlett-type correction for some test statistics under nonnormality"数理解析研究所講究録. 1308. 39-52 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Akahira, M., Takeuchi, K.: "Joint Statistical Papers of Akahira and Takeuchi"World Scientific. 620 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hide, E., Akahira, M.: "An approximation to the generalized hypergeonetric distribution"Statistical Papers. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] Tanaka, H., Akahira, M.: "One family of distributions attaining the Bhattachryya bound"Ann. Inst. Statist. Math.. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] 飛田英祐, 赤平昌文: "記録値に対する予測区間の構成について"数理解析研究所講究録. 1273. 165-177 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Koike, K.: "On the inequality of kshirsagar"Commun. Statist. -Theory Math.. 31・9. 1617-1627 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 小池健一: "不偏推定量の分散に関するChapman-Robbins型不等式の拡張について"数理解析研究所講究録. 1273. 124-137 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 青木充, 甲斐正樹, 青嶋 誠: "Note on sample size determination for detecting the worst component of a multivariate exponential distribution"数理解析研究所講究録. 1273. 138-147 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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