Nonparametric multivariate boundary-bias-free density estimation and its application

• Project/Area Number: 15H06068
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Economic statistics
• Research Institution: University of Tsukuba
• Principal Investigator: IGARASHI Gaku 筑波大学, システム情報系, 助教 (40759346)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2016: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: ノンパラメトリック密度推定 / 統計科学

Outline of Final Research Achievements

We focused on nonparametric density estimation when the support of the estimated density has the boundary. We proposed multivariate log-normal kernel density estimator and its generalization, using the idea of the weighted distribution, and derived their asymptotic properties. We also proposed inverse gamma and Amoroso kernel density estimators, and derived their asymptotic properties. Furthermore, we discussed the bias-reduced beta and Amoroso kernel density estimators. Simulation studies and data analyses were conducted to illustrate the asymptotic results.

Research Products

• [Journal Article] Inverse gamma kernel density estimation for nonnegative data (2017)
  • Author(s): Kakizawa, Yoshihide and Igarashi, Gaku
  • Journal Title: Journal of the Korean Statistical Society Volume: 印刷中 Issue: 2 Pages: 194-207
  • DOI: 10.1016/j.jkss.2016.09.002
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Bias reductions for beta kernel estimation (2016)
  • Author(s): Gaku Igarashi
  • Journal Title: Journal of Nonparametric Statistics Volume: 28 Issue: 1 Pages: 1-30
  • DOI: 10.1080/10485252.2015.1112011
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Amoroso カーネル密度推定量とその改良について (2017)
  • Author(s): 五十嵐岳, 柿沢佳秀
  • Organizer: 研究集会「第18回ノンパラメトリック統計解析とベイズ統計」
  • Place of Presentation: 慶應義塾大学(東京都港区)
  • Year and Date: 2017-03-28
• [Presentation] 境界バイアスのない非対称カーネル密度推定量について (2017)
  • Author(s): 五十嵐岳
  • Organizer: 日本数学会2017年度年会
  • Place of Presentation: 首都大学東京(東京都八王子市)
  • Year and Date: 2017-03-26
  • Invited
• [Presentation] Amoroso カーネルを用いたノンパラメトリック密度推定について (2016)
  • Author(s): 五十嵐岳, 柿沢佳秀
  • Organizer: 2016年度統計関連学会連合大会
  • Place of Presentation: 金沢大学(石川県金沢市)
  • Year and Date: 2016-09-07
• [Presentation] Some boundary-bias-free density estimators (2016)
  • Author(s): Kakizawa, Yoshihide and Igarashi, Gaku
  • Organizer: The 4th Institute of Mathematical Statistics Asia Pacific Rim Meeting
  • Place of Presentation: The Chinese University of Hong Kong (香港)
  • Year and Date: 2016-06-28
  • Int'l Joint Research / Invited
• [Presentation] 多変量加重対数正規カーネルを用いた非対称カーネル推定について (2016)
  • Author(s): 五十嵐岳
  • Organizer: 研究集会「第17回ノンパラメトリック統計解析とベイズ統計」
  • Place of Presentation: 慶應義塾大学三田キャンパス(東京都)
  • Year and Date: 2016-03-29
• [Presentation] 多変量対数正規カーネルを用いた境界バイアスのない密度推定について (2016)
  • Author(s): 五十嵐岳
  • Organizer: 日本数学会2016 年度年会
  • Place of Presentation: 筑波大学(茨城県)
  • Year and Date: 2016-03-17
• [Presentation] Recent developments in boundary-bias-free asymmetric kernel density estimation (2015)
  • Author(s): Kakizawa, Y. and Igarashi, G.
  • Organizer: 研究集会「Recent Progress in Time Series and Related Fields」
  • Place of Presentation: 東北大学(宮城県)
  • Year and Date: 2015-12-11
• [Presentation] 多変量対数正規カーネルを用いた境界バイアスのない密度推定について (2015)
  • Author(s): 五十嵐岳
  • Organizer: 2015 年度統計関連学会連合大会
  • Place of Presentation: 岡山大学 津島キャンパス(岡山県)
  • Year and Date: 2015-09-08