Asymptotic Expansions for U- and V-statistics with Degenerate Kernels

• Project/Area Number: 25400211
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tokyo City University
• Principal Investigator: Kanagawa Shuya 東京都市大学, 共通教育部, 教授 (50185899)
• Co-Investigator(Kenkyū-buntansha): 前園 宜彦 九州大学, 数理学研究院, 教授 (30173701) ; 税所 康正 広島大学, 工学研究科, 准教授 (70195973)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: Symmetric Statistics / Central Limit Theorem / Asymptotic Expansion / U-statistics / V-statistics / Edgeworth expansion / 対称統計量 / 退化型対称統計量 / エッジワース展開 / Cramer-Von Mises統計量 / 従属確率変数列 / 混合性 / 漸近展開 / U-統計量 / V-統計量 / 中心極限定理 / ヒルベルト空間値確率変数 / 対称統計量の漸近理論 / 時系列モデル / 数理ファイナンス / ボラティリティ推定 / 確率微分方程式 / オイラー・丸山近似 / 従属確率変数 / 変化点解析 / 拡散過程 / 複合ポアソン過程 / 時系列データ / 非線形シュレディンガー方程式 / 信頼区間

Outline of Final Research Achievements

We consider asymptotically normal statistics which are symmetric functions of N i.i.d. random variables. For these statistics we prove the va- lidity of an Edgeworth expansion with remainder of the large order of n to the power of (-2) under Cramer’s condition on the linear part of the statistic and moment assumptions for all parts of the statistic. By means of a counterexample we show that it is generally not possible to obtain an Edgeworth expansion with remainder of the large order of n to the power of (-2) without imposing additional assumptions on the structure of the nonlinear part of the statistic.

Research Products

• [Journal Article] Asymptotic properties of a kernel type estimator of a density ratio (2017)
  • Author(s): T. Moriyama and Y. Maesono
  • Journal Title: Bulletin of Informatics and Cybernetics Volume: 49 Pages: 53-66
  • Peer Reviewed
• [Journal Article] 日経225平均株価指数の日次収益率分析におけるジャンプ拡散過程モデルの同定とその低頻度で振幅の大きなジャンプ時点推定への応用について (2016)
  • Author(s): 金川秀也、石田真之
  • Journal Title: 日本経営工学会論文誌 Volume: 67 Pages: 1-9
  • NAID: 130005155919
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Optimal portfolios based on weakly dependent data (2015)
  • Author(s): H. Takahashi, T. Saigo, S. Kanagawa and K. Yoshihara
  • Journal Title: Dynamical Systems and Differential Equations, AIMS Volume: DCDS Supplement Pages: 1041-1049
  • DOI: 10.3934/proc.2015.1041
  • Peer Reviewed / Open Access
• [Journal Article] Asymptotic behavior of solutions of some difference equations (2015)
  • Author(s): H. Takahashi, S. Kanagawa and K. Yoshihara
  • Journal Title: Stochastic Analysis and Applications Volume: 33 Issue: 4 Pages: 740-755
  • DOI: 10.1080/07362994.2015.1038840
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Identification of Jump Times of Large Jumps for the Nikkei 225 Stock Index from Daily Share Prices via a Stochastic Volatility Model (2015)
  • Author(s): S. Ishida and S. Kanagawa
  • Journal Title: Theoretical and Applied Mechanics Japan Volume: 63 Issue: 0 Pages: 109-116
  • DOI: 10.11345/nctam.63.109
  • NAID: 130005103441
  • ISSN: 1348-0693, 1349-4244
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Optimal portfolios based on weakly dependent data (2015)
  • Author(s): H. Takahashi, T. Saigo, S. Kanagawa and K. Yoshihara
  • Journal Title: Dynamical Systems and Differential Equations, DCDS Supplement 2015, AIMS Volume: Supplement Volume
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Estimation of Jump Times of Large Jumps for the Nikkei 225 Stock Index from Daily Share Prices by a Stochastic Volatility Model (2015)
  • Author(s): S. ISHIDA and S. KANAGAWA
  • Journal Title: Theoretical and Applied Mechanics Japan Volume: 63
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] The nonlinear Schrodinger equation created by the vibrations of an elastic plate and its dimensional expansion (2014)
  • Author(s): S. Kanagawa and B. T. Nohara
  • Journal Title: Dynamical Systems and Differential Equations, DCDS Supplement 2013, AIMS Volume: Supplement Volume Pages: 415-426
  • NAID: 40019298858
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A Confidence Interval for the Euler-Maruyama Approximate Solution of SDE with Unbounded Coefficients (2014)
  • Author(s): S. Kanagawa and S. Hasegawa
  • Journal Title: Theoretical and Applied Mechanics Japan Volume: 62 Pages: 91-98
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] The Euler-Maruyama Approximation for the Reflecting Ornstein-Uhlenbeck Process Using the Penalty Method (2013)
  • Author(s): S. Kanagawa
  • Journal Title: Theoretical and Applied Mechanics Japan Volume: 61 Pages: 207-213
  • Peer Reviewed
• [Journal Article] The nonlinear Schrodinger equation created by the vibriation of an elastic plate and its dimensional expansion (2013)
  • Author(s): S. Kanagawa and B. T. Nohara
  • Journal Title: Discrete and Continuous Dynamical Systems Volume: Supplement Volume Pages: 415-426
  • Peer Reviewed
• [Journal Article] Mathematical models of the generation of radiation-induced DNA double-strand breaks (2013)
  • Author(s): Y. Saisho and A. Ito
  • Journal Title: Journal of Mathematical Biology Volume: 67 Pages: 717-736
  • Peer Reviewed
• [Journal Article] DNA 2本鎖切断生成の確率モデル (2013)
  • Author(s): 税所 康正,伊藤 敦
  • Journal Title: 数理解析研究所講究録 Volume: 1853 Pages: 202-209
• [Presentation] 株価ボラティリティ推定に関する新提案 (2018)
  • Author(s): 金川 秀也
  • Organizer: 第182回ファジィ科学シンポジウム
• [Presentation] Estimation of Jump-Times of Daily Share Prices of Nikkei 225 Stock Index Using a Jump Diffusion Model (2017)
  • Author(s): S. Kanagawa
  • Organizer: NCTS Workshop on Applied Analysis and Probability
  • Place of Presentation: Taipei (Taiwan)
  • Year and Date: 2017-03-24
  • Int'l Joint Research / Invited
• [Presentation] Time Series Analysis of Cerebral Blood Flow Data Measured by Light Topography (2017)
  • Author(s): S. Kanagawa
  • Organizer: 第30回バイオメディカル・ファジィ・システム学会年次大会
• [Presentation] (3) Optimal portfolios based on weakly dependent data (2016)
  • Author(s): S. Kanagawa
  • Organizer: The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Orlando (USA)
  • Year and Date: 2016-07-01
  • Int'l Joint Research / Invited
• [Presentation] Identification of jump times of large jumps for the Nikkei 225 stock index from daily share prices via a stochastic volatility model (2016)
  • Author(s): S. Kanagawa
  • Organizer: High Dimensional Statistical Analysis & Quantile Analysis for Time Series
  • Place of Presentation: 熊本大学 （熊本）
  • Year and Date: 2016-03-03
  • Int'l Joint Research / Invited
• [Presentation] Estimation of Jump-Times of a Jump Diffusion Model for Nikkei 225 Stock Index (2015)
  • Author(s): S. Kanagawa
  • Organizer: Seventh International Conference on Dynamic Systems and Applications & Fifth International Conference on Neural, Parallel, and Scientific Computations
  • Place of Presentation: Morehouse College, Atlanta, USA
  • Year and Date: 2015-05-27
  • Int'l Joint Research / Invited
• [Presentation] How to find jump-times of a Black-Scholes model with jumps for Nikkei 225 stock index (2014)
  • Author(s): S. Kanagawa
  • Organizer: ICM Satellite Conference 2014: The Fourth Asian Conference on Nonlinear Analysis and Optimization
  • Place of Presentation: Taipei, Taiwan
  • Year and Date: 2014-08-05 – 2014-08-09
• [Presentation] On the mathematical models describing the generation of DNA damages by radiation (2014)
  • Author(s): Y. Saisho
  • Organizer: ICM Satellite Conference 2014: The Fourth Asian Conference on Nonlinear Analysis and Optimization
  • Place of Presentation: Taipei, Taiwan
  • Year and Date: 2014-08-05 – 2014-08-09
• [Presentation] S-continuous financial time series composed from the delta-function (2014)
  • Author(s): S. Kanagawa
  • Organizer: The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Madrid, Spain
  • Year and Date: 2014-07-07 – 2014-07-11
  • Invited
• [Presentation] Optimal portfolios based on weakly dependent data (2014)
  • Author(s): S. Kanagawa
  • Organizer: The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Madrid, Spain
  • Year and Date: 2014-07-07 – 2014-07-11
  • Invited
• [Presentation] Stochastic models describing the generation of dsbs of DNA by radiation, (2014)
  • Author(s): Y. Saisho
  • Organizer: The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Madrid, Spain
  • Year and Date: 2014-07-07 – 2014-07-11
  • Invited
• [Presentation] How to teach a concept of probability? (2013)
  • Author(s): S. Kanagawa
  • Organizer: Taiwan-Japan Bilateral Symposium on Mathematics Education
  • Place of Presentation: 台湾国立師範大学、台北、台湾
• [Presentation] 放射線による DNA 2本鎖切断生成を表現する確率モデルについて
  • Author(s): 税所 康正
  • Organizer: 第50 回放射線影響懇話会
  • Place of Presentation: 佐賀大学
  • Invited
• [Presentation] 放射線による DNA 切断生成の数理モデル
  • Author(s): 税所 康正, 伊藤 敦
  • Organizer: 第 23 回日本数理 生物学会大会・企画シンポジウム「放射線によるDNA損傷問題の周辺 ― 数理モデ ルの可能性と役割」
  • Place of Presentation: 静岡大学
• [Book] 改訂版 日本産セミ科図鑑 (2015)
  • Author(s): 林 正美，税所 康正
  • Total Pages: 224
  • Publisher: 誠文堂新光社
• [Book] 理工系学生のための確率・統計講義 (2014)
  • Author(s): 金川秀也、吉田稔、堀口正之
  • Total Pages: 165
  • Publisher: 培風館
• [Book] 理工系学生のための確率・統計講義 (2014)
  • Author(s): 金川秀也、吉田 稔、堀口正之
  • Total Pages: 171
  • Publisher: 培風館