Theory of asymptotic analysis in statistics

• Project/Area Number: 17H01702
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• 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): 2017-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥15,990,000 (Direct Cost: ¥12,300,000、Indirect Cost: ¥3,690,000); Fiscal Year 2020: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2019: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2018: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2017: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
• Keywords: 確率過程 / 漸近展開 / 擬似尤度解析 / マリアバン解析 / 非エルゴード統計 / 高頻度データ / 漸近理論 / 尤度解析 / 高頻度観測 / フラクショナルブラウン運動 / 確率微分方程式 / Euler-Maruyama近似 / ジャンプ / 退化拡散過程 / Wiener汎関数 / Skorohod積分 / スパース推定 / 極限定理 / モデル選択 / リード・ラグ / 統計数学 / 確率論

Outline of Final Research Achievements

The basic theory of asymptotic analysis in statistical inference for stochastic processes was pursued. Theory of asymptotic expansions for Wiener functionals both in ergodic and non-ergodic statistics was studied, which is the basis of higher-order asymptotic theories. The developed techniques led to asymptotic expansions for Skorohod integrals and general Wiener functionals. Also this project deepened the theory of quasi-likelihood analysis toward applications to various stochastic processes and sparse estimation.

Academic Significance and Societal Importance of the Research Achievements

ここで発展した確率過程に対する漸近展開理論は、エルゴード系および非エルゴード系におけるウイナー汎関数の分布論的漸近展開という今までになかった領域に踏み込んだものであり、確率論および数理統計学における極限定理研究の新しい局面を切り拓いた。本研究の統計推測論的側面として、擬似尤度解析の深化と応用は、確率過程の統計推測論をさらに発展させている。これらの結果は、従属性データの解析というデータサイエンスのさまざまな場面で応用可能な統計数理の基礎になるものである。

Research Products

• [Int'l Joint Research] Universite de Lille/Universite Evry Val d'Essonne/Universite Paris-Saclay(フランス)
• [Int'l Joint Research] Linkoping University(スウェーデン)
• [Int'l Joint Research] Universite Paris 1/Universite Evry Val d'Exxonne/Universite de Lille(フランス)
• [Int'l Joint Research] University of Milan(イタリア)
• [Int'l Joint Research] Aarhus University(デンマーク)
• [Int'l Joint Research] University of Kansas(米国)
• [Int'l Joint Research] Universite Paris 1/Universite Evry Val-d'Essonne(フランス)
• [Int'l Joint Research] University of Milan(イタリア)
• [Int'l Joint Research] Aarhus University(デンマーク)
• [Int'l Joint Research] University of Kansas(米国)
• [Journal Article] Asymptotic expansion and estimates of Wiener functionals (2023)
  • Author(s): Yoshida, N.
  • Journal Title: Stochastic Processes and their Applications Volume: 157 Pages: 176-248
  • DOI: 10.1016/j.spa.2022.10.003
  • Peer Reviewed / Open Access
• [Journal Article] Quasi-likelihood analysis and its applications (2022)
  • Author(s): Yoshida, N.
  • Journal Title: Statistical Inference for Stochastic Processes Volume: 25 Issue: 1 Pages: 43-60
  • DOI: 10.1007/s11203-021-09266-0
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Divergence of an integral of a process with small ball estimate (2022)
  • Author(s): Mishura, Y., Yoshida, N.
  • Journal Title: Stochastic Processes and their Applications Volume: 148 Pages: 1-24
  • DOI: 10.1016/j.spa.2022.02.006
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Marked point processes and intensity ratios for limit order book modeling (2022)
  • Author(s): Muni Toke, I., Yoshida, N
  • Journal Title: Japanese Journal of Statistics and Data Science Volume: 5 Issue: 1 Pages: 1-39
  • DOI: 10.1007/s42081-021-00137-9
  • NAID: 210000178425
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Adaptive estimation for degenerate diffusion processes (2021)
  • Author(s): Gloter, A., Yoshida, N.
  • Journal Title: Electronic Journal of Statistics Volume: 15 Issue: 1 Pages: 1424-1472
  • DOI: 10.1214/20-ejs1777
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Global jump filters and quasi likelihood analysis for volatility (2021)
  • Author(s): Inatsugu, H., Yoshida, N.
  • Journal Title: Annals of the Institute of Statistical Mathematics Volume: 73 Issue: 3 Pages: 555-598
  • DOI: 10.1007/s10463-020-00768-x
  • Peer Reviewed
• [Journal Article] Edgeworth expansion for Euler approximation of continuous diffusion processe (2020)
  • Author(s): Podolskij, M., Veliyev, B., Yoshida, N.
  • Journal Title: Annals of Applied Probability Volume: 30 Issue: 4 Pages: 1971-2003
  • DOI: 10.1214/19-aap1549
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Asymptotic expansion of the quadratic variation of a mixed fractional Brownian motion (2020)
  • Author(s): Tudor, C., Yoshida, N.
  • Journal Title: Statistical Inference for Stochastic Processes Volume: 23 Issue: 2 Pages: 435-463
  • DOI: 10.1007/s11203-020-09220-6
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Analyzing order flows in limit order books with ratios of Cox-type intensities (2020)
  • Author(s): Muni Toke Ioane、Yoshida Nakahiro
  • Journal Title: Quantitative Finance Volume: 20 Issue: 1 Pages: 81-98
  • DOI: 10.1080/14697688.2019.1637927
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Penalized least squares approximation methods and their applications to stochastic processes (2020)
  • Author(s): Suzuki Takumi、Yoshida Nakahiro
  • Journal Title: Japanese Journal of Statistics and Data Science Volume: - Issue: 2 Pages: 513-541
  • DOI: 10.1007/s42081-019-00064-w
  • NAID: 210000179867
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Asymptotic expansion of Skorohod integrals (2019)
  • Author(s): Nualart David、Yoshida Nakahiro
  • Journal Title: Electronic Journal of Probability Volume: 24 Issue: none Pages: 1-64
  • DOI: 10.1214/19-ejp310
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos (2019)
  • Author(s): Tudor Ciprian A.、Yoshida Nakahiro
  • Journal Title: Stochastic Processes and their Applications Volume: 129 Issue: 9 Pages: 3499-3526
  • DOI: 10.1016/j.spa.2018.09.018
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Statistical inference for ergodic point processes and application to Limit Order Book (2018)
  • Author(s): Clinet, Simon and Yoshida, Nakahiro
  • Journal Title: Stochastic Processes and Their Applications Volume: 127 Pages: 1800-1839
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Edgeworth expansion for the pre-averaging estimator (2018)
  • Author(s): Podolskij, M., (Aarhus University), Veliyev. B., (Aarhus University), Yoshida, N (University of Tokyo)
  • Journal Title: Stochastic Processes and their Applications Volume: 127 Pages: 3558-3595
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Partial quasi-likelihood analysis (2018)
  • Author(s): Yoshida Nakahiro
  • Journal Title: Japanese Journal of Statistics and Data Science Volume: 1 Issue: 1 Pages: 157-189
  • DOI: 10.1007/s42081-018-0006-6
  • NAID: 210000164710
  • Peer Reviewed
• [Presentation] Adaptive and non-adaptive estimation for degenerate diffusion processes (2022)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Statistics of Stochastic Processes in Discrete and Continuous Time
  • Int'l Joint Research / Invited
• [Presentation] Simplified quasi-likelihood analysis (2022)
  • Author(s): Yoshida, Nakahiro
  • Organizer: DYNSTOCH 2022
  • Int'l Joint Research
• [Presentation] Asymptotic expansion in volatility parametric estimation revisited (2022)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Scale Invariance and Randomness,
  • Int'l Joint Research / Invited
• [Presentation] Asymptotic expansion of variations (2022)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Seminar - ANR EFFI
  • Int'l Joint Research / Invited
• [Presentation] Recent developments in the theory of asymptotic expansion. (2021)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Modern Stochastics: Theory and Applications
  • Int'l Joint Research / Invited
• [Presentation] Ibragimov-Khasminskii theory and recent developments in statistical inference for stochastic processes (2021)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Advances in Stochastics & Statistics in honor of Rafail Z. Khasminskii 90th anniversary
  • Int'l Joint Research / Invited
• [Presentation] Global jump filters and realized volatility (2021)
  • Author(s): Yoshida, Nakahiro
  • Organizer: ISI World Statistics Congress 2021
  • Int'l Joint Research / Invited
• [Presentation] Adaptive estimation for a degenerate diffusion process (2021)
  • Author(s): Yoshida, Nakahiro
  • Organizer: 日本数学会秋季総合分科会
• [Presentation] Edgeworth expansion for the EulerMaruyama approximation (2021)
  • Author(s): Yoshida, Nakahiro
  • Organizer: 日本数学会秋季総合分科会
• [Presentation] Asymptotic expansion in volatility parametric estimation revisited (2021)
  • Author(s): Yoshida, Nakahiro
  • Organizer: SMSP2021: Statistical Modeling for Stochastic Processes and related fields
  • Int'l Joint Research / Invited
• [Presentation] Asymptotic expansion in volatility parametric estimation revisited (2021)
  • Author(s): Yoshida, Nakahiro
  • Organizer: CMStatistics 2021
  • Int'l Joint Research / Invited
• [Presentation] Quasi-likelihood analysis for stochastic differential equations: volatility estimation and global jump filters (2021)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Asia-Pacific Seminar in Probability and Statistics
  • Int'l Joint Research / Invited
• [Presentation] Non-adaptive estimation for a degenerate diffusion (2020)
  • Author(s): Yoshida, Nakahiro
  • Organizer: The 13th International Conference of the ERCIM WG (CMStatistics 2020)The 13th International Conference of the ERCIM WG (CMStatistics 2020)
  • Int'l Joint Research / Invited
• [Presentation] Global jump filters and quasi-likelihood analysis for volatility (2019)
  • Author(s): Yoshida, Nakahiro
  • Organizer: DynStoch2019
  • Int'l Joint Research
• [Presentation] Adaptive and non-adaptive estimation of degenerate diffusion processes (2019)
  • Author(s): Yoshida, Nakahiro
  • Organizer: The THIRD YUIMA Conference
  • Int'l Joint Research
• [Presentation] Asymptotic expansion for functionals of a fractional Brownian motion (2019)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Fourth Conference on Ambit Fields and Related Topics
  • Int'l Joint Research / Invited
• [Presentation] Asymptotic expansions in non-ergodic stochastic systems (2019)
  • Author(s): Yoshida, Nakahiro
  • Organizer: 62nd ISI World Statistics Congress 2019
  • Int'l Joint Research / Invited
• [Presentation] 確率統計の統計学の理論と応用 (2019)
  • Author(s): Yoshida, Nakahiro
  • Organizer: 第８回藤原洋数理科学賞授賞式/ピアノコンサート
  • Invited
• [Presentation] Asymptotic expansion of an anticipative functional (2019)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Asymptotic Expansion and Malliavin Calculus II
  • Int'l Joint Research
• [Presentation] Estimation for degernate diffusion processes (2019)
  • Author(s): Yoshida, Nakahiro
  • Organizer: CMStatistics 2019
  • Int'l Joint Research / Invited
• [Presentation] Approaches to asymptotic expansion (2018)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Asymptotic expansion and Malliavin calculus
  • Int'l Joint Research
• [Presentation] Global jump lters and quasi likelihood analysis for volatility (2018)
  • Author(s): Yoshida, Nakahiro
  • Organizer: CMStatistics 2018
• [Presentation] Asymptotic expansion of Skorohod integrals (2018)
  • Author(s): Yoshida, Nakahiro
  • Organizer: ASC2018: Asymptotic Statistics and Computations
  • Int'l Joint Research
• [Presentation] New YUIMA functions to be constructed (2018)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Computational Aspects of Simulation and Inference for Stochastic Processes and the YUIMA Project
  • Int'l Joint Research
• [Presentation] Partial quasi likelihood analysis (2018)
  • Author(s): Yoshida, Nakahiro
  • Organizer: The 5th Institute of Mathematical Statistics Asia Pacific Rim Meeting (APRM)
  • Int'l Joint Research / Invited
• [Presentation] Quasi Likelihood Analysis Of Ratio Models And Limit Order Book (2018)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Dynstoch 2018
  • Int'l Joint Research
• [Presentation] Recent topics in quasi Likelihood analysis (2017)
  • Author(s): Yoshida, Nakahiro
  • Organizer: Dynstoch 2017
  • Int'l Joint Research
• [Presentation] Quasi likelihood analysis and model selection for stochastic processes (2017)
  • Author(s): Yoshida, Nakahiro
  • Organizer: 1st International Conference on Econometrics and Statistics (EcoSta 2017)
  • Int'l Joint Research / Invited
• [Presentation] Penalized methods for stochastic processes (2017)
  • Author(s): Yoshida, Nakahiro
  • Organizer: 10th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2017)
  • Int'l Joint Research / Invited
• [Book] Simulation and Inference for Stochastic Processes with YUIMA (2018)
  • Author(s): Iacus, Stefano M., Yoshida, Nakahiro
  • Total Pages: 268
  • Publisher: Springer
  • ISBN: 9783319555690
• [Funded Workshop] Zoom in YUIMA Tutorial (2020)
• [Funded Workshop] Zoom Asia-Pacific Seminar in Probability and Statistics (2020)
• [Funded Workshop] YUIMA Tutorial (2019)
• [Funded Workshop] The Third YUIMA Conference (2019)
• [Funded Workshop] Asymptotic Expansion and Malliavin Calculus (2019)
• [Funded Workshop] Asymptotic expansion and Malliavin calculus (2018)