Asymptotic expansion, statistical inference and their applications

• Project/Area Number: 19340021
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: The University of Tokyo
• Principal Investigator: YOSHIDA Nakahiro 東京大学, 大学院・数理科学研究科, 教授 (90210707)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥17,550,000 (Direct Cost: ¥13,500,000、Indirect Cost: ¥4,050,000); Fiscal Year 2010: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2009: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2008: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2007: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
• Keywords: 解析学 / 確率論 / 統計数学 / 応用数学 / 経済統計学 / 漸近展開 / 非エルゴード統計 / 混合正規分布 / リードラグ / 疑似尤度解析 / マリアバン解析 / デリバティブ / 適合型推定量 / ボラティリティ / 2次変動 / 条件つき分布 / 非同期共分散 / リード・ラグ / マルチンゲール / 確率微分方程式 / 確率場 / ベイズ推定 / 安定的収束 / 変化点問題 / 疑似尤度 / Malliavin解析

Research Abstract

A quasi likelihood analysis(QLA) was constructed for stochastic differential equations with jumps. Adaptive methods for continuous diffusion type processes were proposed. This gives a basis for implementation. The change point problem was studied for a stochastic regression model, and the limit theorem was presented through a mixture type Gaussian functional. Proof of the asymptotic mixed normality of the nonsynchronous covariance estimator(Hayashi-Yoshida estimator) was published. A lead-lag problem was framed and we proved a convergence rate of our lead-lag estimator for a semimartingale model with lag. A theory of asymptotic expansion for a martingale with mixed normal limit was initiated and applied to the realized volatility.

Research Products

• [Journal Article] Nonsynchronous covariance process and limit theorems (2011)
  • Author(s): T. Hayashi and N. Yoshida
  • Journal Title: Stochastic Processes and their Applications on-line Volume: 121 Pages: 2416-2454
• [Journal Article] Second-order asymptotic expansion for a non-synchronous covariation estimator (2011)
  • Author(s): D. Arnak and N. Yoshida
  • Journal Title: Annales de l' Institut Henri Poincare Volume: 47, 3 Pages: 748-789
• [Journal Article] Asymptotic Expansion for Functionals of a Marked Point Process (2011)
  • Author(s): Y. Sakamoto and N. Yoshida
  • Journal Title: Communications in Statistics-Theory and Methods Volume: 39 Pages: 449-1465
• [Journal Article] Quasi-likelihood analysis for the stochastic differential equation with jumps (2011)
  • Author(s): T. Ogihara and N. Yoshida
  • Journal Title: Statistical Inference for Stochastic Processes Volume: 14 Pages: 189-229
• [Journal Article] Nonsynchronous covariation process and limit theorems (2011)
  • Author(s): Takaki Hayashi, Nakahiro Yoshida
  • Journal Title: Stochastic Processes and their Applications on-line Volume: 121, Issue 10 Pages: 2416-2454
  • Peer Reviewed
• [Journal Article] Second-order asymptotic expansion for a non-synchronous covariation estimator (2011)
  • Author(s): Arnak Dalalyan, Nakahiro Yoshida
  • Journal Title: Annales de l'Institut Henri Poincare-Probabilites et Statistiques Volume: 47, Issue 3 Pages: 748-789
  • Peer Reviewed
• [Journal Article] Quasi-likelihood analysis for the stochastic differential equation with jumps (2011)
  • Author(s): Teppei Ogihara, Nakahiro Yoshida
  • Journal Title: Statistical Inference for Stochastic Processes Volume: 14, Issue 3 Pages: 189-229
  • Peer Reviewed
• [Journal Article] Numerical Analysis of Volatility Change Point Estimators for Discretely Sampled Stochastic Differential Equations (2010)
  • Author(s): S. Iacus and N. Yoshida
  • Journal Title: Economic Notes by Banca Monte dei Paschi di Siena SpA Volume: 39
• [Journal Article] 確率過程の統計学:概観と展望 (2010)
  • Author(s): 吉田朋広
  • Journal Title: 日本統計学会誌 Volume: 40, 1 Pages: 47-60
  • NAID: 110007988944
• [Journal Article] Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations (2010)
  • Author(s): N. Yoshida
  • Journal Title: Annals of the Institute of Statistical Mathematics online
  • NAID: 40018798391
• [Journal Article] Numerical analysis of volatility change point estimators for discretely sampled stochastic differential equations (2010)
  • Author(s): Stefano Iacus, Nakahiro Yoshida
  • Journal Title: Economic Notes by Banca Monte dei Paschi di Siena SpA Volume: 39, Issue1 and 2 Pages: 107-127
  • Peer Reviewed
• [Journal Article] Expansion of the asymptotically conditionally normal law (2010)
  • Author(s): Nakahiro Yoshida
  • Journal Title: Research Memorandam Volume: 1125
  • Peer Reviewed
• [Journal Article] Asymptotic Expansion for Functionals of a Marked Point Process (2010)
  • Author(s): Yuji Sakamoto, Nakahiro Yoshida
  • Journal Title: Communications in Statistics - Theory and Methods Volume: 39 Pages: 1449-1465
  • Peer Reviewed
• [Journal Article] 確率過程の統計学:概観と展望(日本統計学会賞受賞者特別寄稿論文) (2010)
  • Author(s): 吉田朋広
  • Journal Title: 日本統計学会誌 Volume: 40(issue 1) Pages: 47-60
  • Peer Reviewed
• [Journal Article] Third-order asymptotic expansion of M-estimators for diffusion processes (2009)
  • Author(s): Y. Sakamoto and N. Yoshida
  • Journal Title: Annals of the Institute of Statistical Mathematics Volume: 61 Pages: 629-661
  • NAID: 40016772332
• [Journal Article] Estimation for the discretely observed telegraph process (2009)
  • Author(s): S. Iacus and N. Yoshida
  • Journal Title: Theor. Probability and Math. Statist Volume: 78 Pages: 37-47
• [Journal Article] Parametric estimation for partially hidden diffusion processes sampled at discrete times (2009)
  • Author(s): S. Iacus and N. Yoshida
  • Journal Title: Stochastic Processes and their Applications Volume: 119 Pages: 1580-1600
• [Journal Article] Parametric estimation for partially hidden diffusion processes sampled at discrete times (2009)
  • Author(s): S. Iacus, M. Uchida, N. Yoshida
  • Journal Title: Stochastic Processes and their Applications 119 Pages: 1580-1600
• [Journal Article] Estimation for the discretely observed telegraph process (2009)
  • Author(s): Stefano Iacus, Nakahiro Yoshida
  • Journal Title: Theory of Probability and Mathematical Statistics Volume: 78 Pages: 37-47
  • Peer Reviewed
• [Journal Article] Estimation for the discretely observed telegraph process (2009)
  • Author(s): S.M.Iacus, N.Yoshida
  • Journal Title: Theor.Probability and Math.Statist 78 Pages: 37-47
  • Peer Reviewed
• [Journal Article] Parametric estimation for partially hidden diffusion processes sampled at discrete times (2009)
  • Author(s): SM Iacus, M Uchida, N Yoshida
  • Journal Title: Stochastic Processes and their Applications 119 Pages: 1580-1600
  • Peer Reviewed
• [Journal Article] Asymptotic Expansion for Stochastic Processes : an Overview and Examples (2008)
  • Author(s): Y. Sakamoto and N. Yoshida
  • Volume: 38
  • Pages: 173-185
  • NAID: 10030993668
• [Journal Article] Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes (2008)
  • Author(s): T. Hayashi and N. Yoshida
  • Journal Title: Annals of the Institute of Statistical Mathematics Volume: 60 Pages: 367-406
  • NAID: 40016082029
• [Journal Article] Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes (2008)
  • Author(s): T. Hayashi, N. Yoshida
  • Journal Title: Annals of the Institute of Statistical Mathematics 60 Pages: 367-406
  • NAID: 40016082029
• [Journal Article] Asymptotic Expansion for Stochastic Processes : an overview and examples (2008)
  • Author(s): Y. Sakamoto, N. Yoshida
  • Journal Title: J.Japan Statistical Society 38 Pages: 173-185
  • NAID: 10030993668
• [Journal Article] 高頻度金融データと統計科学 (2008)
  • Author(s): 林高樹, 吉田朋広
  • Journal Title: 21世紀の統計科学I : 社会・経済の統計科学 Pages: 267-304
• [Journal Article] Asymptotic Expansion for Stochastic Processes : an Overview and Examples (2008)
  • Author(s): Yuji Sakamoto, Nakahiro Yoshida
  • Journal Title: JOURNAL OF THE JAPAN STATISTICAL SOCIETY 38 Pages: 173-185
  • NAID: 10030993668
  • Peer Reviewed
• [Journal Article] Asymptotic normality of nonsynchronous covariance estimtitors for diffuision processes (2008)
  • Author(s): T.Hayashi and N.Yoshida
  • Journal Title: Annals of the Institute of Statistical Mathematics, to appear (掲載確定)
  • Peer Reviewed
• [Journal Article] Third order asymptotic expansion of M-estimators for diffusion processes (2008)
  • Author(s): Y.Sakamoto and N.Yoshida
  • Journal Title: Annals of the Institute of Statistical Mathematics, to appear (掲載確定)
  • NAID: 40016772332
  • Peer Reviewed
• [Journal Article] On moment estimation for difflsion process (2007)
  • Author(s): Yu.Kutoyants and N.Yoshida
  • Journal Title: Bernoulli 13 Pages: 933-951
  • Peer Reviewed
• [Presentation] Limit theorems in asymptotic statistics for diffusions (2011)
  • Author(s): N. Yoshida
  • Organizer: Asymptotical Statistics of Stochastic Processes VIII
  • Place of Presentation: Universit' e du Maine, Le Mans, France
  • Year and Date: 2011-03-21
• [Presentation] Limit theorems in asymptotic statistics for diffusions (2011)
  • Author(s): Nakahiro Yoshida
  • Organizer: Asymptotical Statistics of Stochastic Processes VIII
  • Place of Presentation: Universit'e du Maine, Le Mans, France
  • Year and Date: 2011-03-21
• [Presentation] Qualsi-likelihood analysis and limit theorems in volatility estimation (2011)
  • Author(s): N. Yoshida
  • Organizer: Statistical inference and numerical analysis of stochastic processes : probabilistic tools and application to financial econometrics Universita' Degli Studi Di Firenze, Novoli
  • Place of Presentation: Firenze, Italy
  • Year and Date: 2011-03-17
• [Presentation] Qualsi-likelihood analysis and limit theorems in volatility estimation (2011)
  • Author(s): Nakahiro Yoshida
  • Organizer: Statistical inference and numerical analysis of stochastic processes : probabilistic tools and application to financial econometrics
  • Place of Presentation: Universita' Degli Studi Di Firenze, Novoli, Firenze, Italy
  • Year and Date: 2011-03-17
• [Presentation] Some limit theorems in inference for volatility. Statistics for Stochastic Processes : Inference, Asymptotic Methods (2011)
  • Author(s): N. Yoshida
  • Organizer: Finance and Data Analysis
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2011-02-23
• [Presentation] Some limit theorems in inference for volatility (2011)
  • Author(s): Nakahiro Yoshida
  • Organizer: Statistics for Stochastic Processes : Inference, Asymptotic Methods, Finance and Data Analysis
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2011-02-23
• [Presentation] Statistical inference for volatility and related limit theorems (2010)
  • Author(s): N. Yoshida
  • Organizer: Asymptotic Statistics, Risk and Computation in Finance and Insurance
  • Place of Presentation: 東京工業大学
  • Year and Date: 2010-12-15
• [Presentation] Statistical inference for volatility and related limit theorems (2010)
  • Author(s): Nakahiro Yoshida
  • Organizer: Asymptotic Statistics, Risk and Computation in Finance and Insurance
  • Place of Presentation: 東京工業大学百年記念会館
  • Year and Date: 2010-12-15
• [Presentation] Statistical inference for volatility and related limit theorems (2010)
  • Author(s): N. Yoshida
  • Organizer: Market Microstructure, Confronting Many Viewpoints
  • Place of Presentation: Institut Louis Bachelier, Paris, France
  • Year and Date: 2010-12-07
• [Presentation] Limit theorems and estimation for diffusions (2010)
  • Author(s): N. Yoshida
  • Organizer: 諸分野との協働による数理科学のフロンティア
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-11-19
• [Presentation] Limit theorems and volatility estimation (2010)
  • Author(s): N. Yoshida
  • Organizer: 数理統計学の新たな展開,大宮ソニックシティー
  • Year and Date: 2010-11-15
• [Presentation] Limit theorems and volatility estimation (2010)
  • Author(s): Nakahiro Yoshida
  • Organizer: 数理統計学の新たな展開
  • Place of Presentation: 大宮ソニックシティー,埼玉
  • Year and Date: 2010-11-15
• [Presentation] Statistical inference for diffusions (2010)
  • Author(s): N. Yoshida
  • Organizer: SPA OSAKA 2010, 34th Conference on Stochastic Processes and Their Applications
  • Place of Presentation: Kyoto Research Park
  • Year and Date: 2010-09-15
• [Presentation] Statistical inference for diffusions (2010)
  • Author(s): Nakahiro Yoshida
  • Organizer: Workshop on "Mathematical finance and related issues"
  • Place of Presentation: 京都リサーチパーク,京都
  • Year and Date: 2010-09-15
• [Presentation] Asymptotic expansion for a martingale with a mixed normal limit distribution (2010)
  • Author(s): N. Yoshida
  • Organizer: SPA OSAKA 2010, 34th Conference on Stochastic Processes and Their Applications
  • Place of Presentation: Senri Life Science Center Building
  • Year and Date: 2010-09-10
• [Presentation] Asymptotic expansion for a martingale with a mixed normal limit distribution (2010)
  • Author(s): Nakahiro Yoshida
  • Organizer: SPA OSAKA 2010, 34th Conference on Stochastic Processes and Their Applications
  • Place of Presentation: 千里ライフサイエンスセンタービル,大阪
  • Year and Date: 2010-09-10
• [Presentation] Inference for Discretely Observed Diffusion Processes (2010)
  • Author(s): N. Yoshida
  • Organizer: 1st R/Rmetrics Summer School and 4th User/Developer Meeting on Computational Finance and Financial Engineering, Meielisalp
  • Place of Presentation: Switzerland
  • Year and Date: 2010-06-29
• [Presentation] Inference for discretely observed diffusion processes (2010)
  • Author(s): Nakahiro Yoshida
  • Organizer: 1st R/Rmetrics Summer School and 4th User/Developer Meeting on Computational Finance and Financial Engineering
  • Place of Presentation: Meielisalp, Switzerland
  • Year and Date: 2010-06-29
• [Presentation] Martingale expansion : mixed normal limit and applications (2010)
  • Author(s): N. Yoshida
  • Organizer: DYNSTOCH meeting
  • Place of Presentation: The University of Angers, France
  • Year and Date: 2010-06-17
• [Presentation] 確率過程の統計学:概観と展望 (2010)
  • Author(s): 吉田朋広
  • Organizer: 第4回日本統計学会春季集会
  • Place of Presentation: 青山学院大学
  • Year and Date: 2010-03-07
• [Presentation] 確率過程の統計学:概観と展望(日本統計学会賞) (2010)
  • Author(s): 吉田朋広
  • Organizer: 第4回日本統計学会春季集会
  • Place of Presentation: 青山学院大
  • Year and Date: 2010-03-07
• [Presentation] Martingale expansion of mixture type and its applications (2010)
  • Author(s): N. Yoshida
  • Organizer: Workshop on "Stochastic Analysis and Statistical Inference V"
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2010-02-22
• [Presentation] 確率過程の漸近展開:概観と展望 (2009)
  • Author(s): 吉田朋広
  • Organizer: 2009年度中之島ワークショップ金融工学・数理・計量ファイナンスの諸問題
  • Place of Presentation: 大阪大学中之島センター
  • Year and Date: 2009-12-05
• [Presentation] 確率過程の漸近展開:概観と展望 (2009)
  • Author(s): 吉田朋広
  • Organizer: 第2009年度中之島ワークショップ 金融工学・数理・計量ファイナンスの諸問題
  • Place of Presentation: 大阪大学中之島センター
  • Year and Date: 2009-12-05
• [Presentation] Asymptotic expansion for a martingale with a mixed normal limit distribution (2009)
  • Author(s): N. Yoshida
  • Organizer: DYNSTOCH Meeting 2009
  • Place of Presentation: Humboldt-Universitat zu Berlin, Germany
  • Year and Date: 2009-10-08
• [Presentation] Asymptotic expansion for a martingale with a mixed normal limit distribution (2009)
  • Author(s): Niakahiro Yoshida
  • Organizer: DYNSTOCH Meeting 2009
  • Place of Presentation: Humboldt-Universitat zu Berlin,ドイツ
  • Year and Date: 2009-10-08
• [Presentation] 確率微分方程式のボラティリティの推定 (2009)
  • Author(s): 内田雅之,吉田朋広
  • Organizer: 2009年度統計関連学会連合大会
  • Place of Presentation: 同志社大学
  • Year and Date: 2009-09-07
• [Presentation] 確率微分方程式のボラティリティの推定 (2009)
  • Author(s): 吉田朋広、内田雅之
  • Organizer: 2009年度 統計関連学会連合大会
  • Place of Presentation: 同志社大学
  • Year and Date: 2009-09-07
• [Presentation] 確率微分方程式の統計学雑感 (2009)
  • Author(s): 吉田朋広
  • Organizer: 平成21年度統計数理研究所共同研究集会統計サマーセミナー2009
  • Place of Presentation: 福井県あわら市芦原温泉
  • Year and Date: 2009-08-12
• [Presentation] 確率微分方程式の統計学 雑感 (2009)
  • Author(s): 吉田朋広
  • Organizer: 平成21年 度統計数理研究所共同研究集会統計サマーセミナー2009
  • Place of Presentation: 福井県あわら市芦原温泉
  • Year and Date: 2009-08-12
• [Presentation] Quasi-likelihood analysis for stochastic processes (2009)
  • Author(s): N. Yoshida
  • Organizer: 2009年度日本数学会年会
  • Place of Presentation: 東京大学駒場キャンパス講堂
  • Year and Date: 2009-03-28
• [Presentation] Nonsynchronous covariation and limit theorems (2009)
  • Author(s): T. Hayashi and N. Yoshida
  • Organizer: 2009年度日本数学会年会
  • Place of Presentation: 東京大学駒場キャンパス講堂
  • Year and Date: 2009-03-28
• [Presentation] Estimation for misspecified ergodic diffusion processes (2009)
  • Author(s): M. Uchida and N. Yoshida
  • Organizer: 2009年度日本数学会年会
  • Place of Presentation: 東京大学駒場キャンパス講堂
  • Year and Date: 2009-03-28
• [Presentation] Asymptotic expansion for the asymptotically conditionally normal law (2009)
  • Author(s): N. Yoshida
  • Organizer: Asymptotical Statistics of Stochastic Processes VII
  • Place of Presentation: Universit' e du Maine, Le Mans
  • Year and Date: 2009-03-16
• [Presentation] Asymptotic expansion for the asymptotically conditionally normal law (2009)
  • Author(s): N.Yoshida
  • Organizer: Asymptotical Statistics of Stochastic Processes VII
  • Place of Presentation: Universite du Maine, Le Mans
  • Year and Date: 2009-03-16
• [Presentation] Estimation of Lag by the nonsynchronous covariance estimator (2008)
  • Author(s): N. Yoshida
  • Organizer: Workshop on "Stochastic Analysis and Statistical Inference III"
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2008-11-26
• [Presentation] Estimation of Lag by the nonsynchronous covariance estimator (2008)
  • Author(s): N.Yoshida
  • Organizer: Workshop on "Stochastic Analysis and Statistical Inference III"
  • Place of Presentation: 東京大学大学院 数理科学研究科
  • Year and Date: 2008-11-26
• [Presentation] First and second order limit theorems in nonsynchronous covariance estimation (2008)
  • Author(s): N. Yoshida
  • Organizer: 日本学術振興会日露共同研究プロジェクト研究集会
  • Place of Presentation: Stochastic analysis of the advanced statistical models
  • Year and Date: 2008-11-04
• [Presentation] First and second order limit theorems in nonsynchronous covariance estimation (2008)
  • Author(s): N.Yoshida
  • Organizer: 日本学術振興会日露共同研究プロジェクト研究集会
  • Place of Presentation: 広島大学
  • Year and Date: 2008-11-04
• [Presentation] Expansion of asymptotically conditionally normal Law (2008)
  • Author(s): N. Yoshida
  • Organizer: Workshop on Finance and related mathematical and statistical issues
  • Place of Presentation: Kyoto Research Park
  • Year and Date: 2008-09-06
• [Presentation] Expansion of asymptotically conditionally normal Law (2008)
  • Author(s): N.Yoshida
  • Organizer: Workshop on "Finance and related mathematical and statistical issues"
  • Place of Presentation: Kyoto Research Park
  • Year and Date: 2008-09-06
• [Presentation] Nonsynchronous covariance estimation and limit theorems (2008)
  • Author(s): N. Yoshida
  • Organizer: Laboratoire d' Analyse et de Math' ematiques Appliqu' ees Universit' e de Marne-la-Vall' ee
  • Place of Presentation: Paris-Est
  • Year and Date: 2008-03-28
• [Presentation] Nonsynchronous covariance estimation and limit theorems (2007)
  • Author(s): N. Yoshida
  • Organizer: 2007年度中之島ワークショップ金融工学・数理・計量ファイナンスの諸問題
  • Place of Presentation: 大阪大学中之島センター
  • Year and Date: 2007-12-02
• [Presentation] Asymptotic expansion of a nonsynchronous covariance estimator (2007)
  • Author(s): N. Yoshida
  • Organizer: Workshop on Stochastic Analysis and Statistical Inference
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2007-11-30
• [Presentation] Covariance estimation under nonsynchronous sampling (2007)
  • Author(s): N. Yoshida
  • Organizer: DMHF2007 : COE Conference on the Development of Dynamic Mathematics with High Functionality
  • Place of Presentation: Fukuoka
  • Year and Date: 2007-10-03
• [Presentation] Covariance estimation under nonsynchronous sampling (2007)
  • Author(s): Nakahiro Yoshida
  • Organizer: DMHF 2007:COE Conference on the Development of Dynamic Mathematics with High Functionality
  • Place of Presentation: 福岡
  • Year and Date: 2007-10-03
• [Presentation] Limit theorems for non-synchronously sampled diffusion processes (2007)
  • Author(s): N. Yoshida
  • Organizer: 日本学術振興会日露共同研究プロジェクト研究集会「確率的複雑系に対する漸近理論とその応用の研究」
  • Place of Presentation: 大阪大学大学院基礎工学研究科
  • Year and Date: 2007-08-09
• [Remarks]
  • URL: http://www2.ms.u-tokyo.ac.jp/probstat/
• [Remarks]
  • URL: http://www2.ms.u-tokyo.ac.jp/probstat/
• [Remarks]
  • URL: http:///www2.ms.u-tokyo.ac.jp/probstat/