Statistically asymptotic theory for stochastic differential equations and its applications

• Project/Area Number: 19540137
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka University
• Principal Investigator: UCHIDA Masayuki Osaka University, 大学院・基礎工学研究科, 准教授 (70280526)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2007: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
• Keywords: 統計数学 / 拡散過程 / 高頻度データ / 統計的モデリング / パラメータ推定 / 情報量規準 / 離散観測 / ミススペシフィケーション

Research Abstract

離散観測に基づく確率微分方程式モデルの統計的漸近理論について研究し, その応用としてエルゴード性をもつ拡散過程モデルに対する統計的モデル評価規準(赤池型情報量規準)の構成及びその理論的正当化を行った. また, 統計モデルとして仮定した確率微分方程式が真のモデルを含むとは限らない場合(misspecified case)について, 疑似尤度関数を構成し, 擬似最尤推定量の漸近的性質を示した.

Research Products

• [Journal Article] Estimation of a drift parameter for a small diffusion process(in Japanese) (2009)
  • Author(s): Uchida, M.
  • Journal Title: Proceedings of the Institute of Statistical Mathematics (In press) Pages: 15-15
  • Peer Reviewed
• [Journal Article] Parametric estimation for partially hidden diffusion processes sampled at discrete times (2009)
  • Author(s): Iacus, S. M., Uchida, M. and Yoshida, N.
  • Journal Title: Stochastic Processes and their Applications 119 Pages: 1580-1600
  • Peer Reviewed
• [Journal Article] Statistical inference for diffusion processes from discrete observations. (in Japanese) (2008)
  • Author(s): Uchida, M.
  • Journal Title: Sugaku 60 Pages: 368-379
  • Peer Reviewed
• [Journal Article] Approximate martingale estimating functions for stochastic differential equations with small noises (2008)
  • Author(s): Uchida, M.
  • Journal Title: Stochastic Processes and their Applications 118 Pages: 1706-1721
  • Peer Reviewed
• [Journal Article] Parametric estimation for stochastic differential equations. (in Japanese) (2008)
  • Author(s): Uchida, M.
  • Journal Title: Statistical Sciences in the 21st Century III, (eds. G. Kitagawa and A. Takemura). University of Tokyo Press, Tokyo Pages: 179-206
  • Peer Reviewed
• [Journal Article] Approximate martingale estimating functions for stochastic differential equations with small noises. (2008)
  • Author(s): Uchida, M.
  • Journal Title: Stochastic Processes and their Applications 118 Pages: 1706-1721
  • Peer Reviewed
• [Journal Article] Sstatistical inference for diffusion processes from discrete observations. (in Japanese). (2008)
  • Author(s): Uchida, M.
  • Journal Title: Sugaku 60 Pages: 368-379
  • Peer Reviewed
• [Journal Article] Parametric estimation for partially hidden diffusion processes sampled at discrete times.
  • Author(s): Iacus, S. M, et al.
  • Journal Title: Stochastic Processes and their Applications (印刷中)
  • Peer Reviewed
• [Journal Article] Approximate martingale estimating functions for stochastic differential equations with small noises
  • Author(s): Uchida, M.
  • Journal Title: Stochastic Process. Appl. (印刷中)
  • Peer Reviewed
• [Presentation] Asymptotic property of AIC for discretely observed ergodic diffusions (2008)
  • Author(s): Uchida, M.
  • Organizer: 研究集会「確率解析と統計的推測III」
  • Place of Presentation: 東京大学
  • Year and Date: 2008-11-27
• [Presentation] Estimation for discretely observed ergodic diffusions under completely misspecified models (2008)
  • Author(s): Uchida, M.
  • Organizer: 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] Estimation for misspecified diffusion processes from discrete observations (2008)
  • Author(s): Uchida, M.
  • Organizer: Workshop on Statistical Methods for Dynamical Stochastic Models
  • Place of Presentation: University of Padova, Italy
  • Year and Date: 2008-06-26
• [Presentation] Approximate martingale estimating functions for stochastic differential equations with small noises (2007)
  • Author(s): Uchida, M.
  • Organizer: 研究集会「確率解析と統計的推測」
  • Place of Presentation: 東京大学
  • Year and Date: 2007-11-30
• [Presentation] Approximate martingale estimating functions for stochastic differential equations with small noises (2007)
  • Author(s): Uchida, M.
  • Organizer: 統計数理研究所共同研究(重点型研究)研究集会
  • Place of Presentation: 東京大学
  • Year and Date: 2007-11-30
• [Presentation] Estimation for misspecified ergodic diffusion processes (2007)
  • Author(s): 内田雅之
  • Organizer: 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
  • Year and Date: 2007-08-08
• [Presentation] Estimation for misspecified ergodic diffusion processes (2007)
  • Author(s): 内田雅之
  • Organizer: 日露共同研究プロジェクト研究集会
  • Place of Presentation: 大阪大学
  • Year and Date: 2007-08-08