Theory and application of a Bayesian information criterion

• Project/Area Number: 24740069
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Takasaki City University of Economics
• Principal Investigator: Miyata Yoichi 高崎経済大学, 経済学部, 准教授 (10514250)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: ラプラス近似 / ベイズ統計学 / 情報量規準 / 統計的漸近理論 / 漸近理論

Outline of Final Research Achievements

When applying Laplace's method to approximate an integral, we require an exact mode of its integrand. We derive a Laplace approximation using an asymptotic mode of an asymptotic mode instead of the exact mode, and present some ways to establish asymptotic modes with a desirable order.
The class of the asymptotic modes is wide and includes consistent estimators with some convergence rate and a true parameter.

Research Products

• [Presentation] Some asymptotic properties of Bayesian information criteria in misspecified models (2015)
  • Author(s): Yoichi MIYATA
  • Organizer: Waseda International Symposium “High Dimensional Statistical Analysis for Spatio-Temporal Processes and Quantile Analysis for Time Series
  • Place of Presentation: 早稲田大学
  • Year and Date: 2015-11-09
  • Int'l Joint Research
• [Presentation] The validity of Bayesian information criteria in misspecified models (2015)
  • Author(s): Yoichi MIYATA
  • Organizer: Joint Statistical Meetings
  • Place of Presentation: Washington State Convention Center, 800 Convention Place, Seattle
  • Year and Date: 2015-07-29
  • Int'l Joint Research
• [Presentation] The validity of Bayesian information criteria in misspecified models (2015)
  • Author(s): Yoichi MIYATA
  • Organizer: Waseda International Symposium
  • Place of Presentation: Waseda University
  • Year and Date: 2015-03-04
• [Presentation] 一般化BIC における最近の動向とその漸近的な性質について (2014)
  • Author(s): 宮田庸一
  • Organizer: 科研費シンポジウム「統計的推測の理論的基礎とその応用」
  • Place of Presentation: 筑波大学
  • Year and Date: 2014-12-01
• [Presentation] ベイズ型推定量の漸近的な性質について (2014)
  • Author(s): 宮田庸一
  • Organizer: 日本数学会2014年度秋季総合分科会
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-27
  • Invited
• [Presentation] Asymptotic Properties of Bayesian Type Estimators When It Is Not Assumed the Hessian Matrices of Contrast Functions Converge (2014)
  • Author(s): Yoichi MIYATA
  • Organizer: Joint Statistical Meeting
  • Place of Presentation: Boston Convention and Exhibition Center
  • Year and Date: 2014-08-06
• [Presentation] Asymptotic properties of Bayesian type estimators without assuming that the Hessian matrices of log-likelihood functions converge (2013)
  • Author(s): 宮田庸一
  • Organizer: 科研費研究集会「非対称・非線形統計理論と経済・生体科学 への応用」
  • Place of Presentation: 金沢大学サテライトプラザ
• [Presentation] Asymptotic properties of Bayesian analysis in dichotomous logit models (2013)
  • Author(s): Yoichi MIYATA
  • Organizer: The 5th Seminar on Time Series and Financial Engineering
  • Place of Presentation: 東京理科大学 森戸記念館
• [Presentation] 周辺尤度に対するルートn一致推定量を用いたラプラス近似について
  • Author(s): 宮田 庸一
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 北海道大学
• [Presentation] √n一致推定量を用いたベイズ型情報量基準の漸近誤差について
  • Author(s): 宮田 庸一
  • Organizer: The 4th Seminar on Time Series and Financial Engineering
  • Place of Presentation: 早稲田大学早稲田キャンパス