A circular stochastic process with asymmetric errors

• Project/Area Number: 22740076
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: KATO Shogo 統計数理研究所, 大学共同利用機関等の部局等, 助教 (60468535)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 統計数学 / 円周上のデータ / 非対称分布 / 確率過程 / 自己回帰過程 / 国際研究者交流

Research Abstract

Time series of circular data arise in a number of scientific fields. For example, a series of wind directions measured hourly at a weather station can be considered an example of time series of circular data. Another example is a time series of directions of movements of migratory birds observed in biology. In our study we have proposed a circular autoregressive process with asymmetric angular errors and investigated some properties of the proposed process. An application of the proposed model has been briefly discussed.

Research Products

• [Journal Article] An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion (2013)
  • Author(s): Kato, S. and Jones, M.C.
  • Journal Title: Bernoulli Volume: 19 Issue: 1 Pages: 154-171
  • DOI: 10.3150/11-bej397
  • Peer Reviewed
• [Journal Article] 円周上のコーシー分布と関連した統計モデル (2012)
  • Author(s): 加藤昇吾
  • Journal Title: 日本数学会 2012年度 秋季総合分科会 講演アブストラクト Pages: 105-121
  • NAID: 130006026483
• [Journal Article] Robust estimation of location and concentration parameters for the von Mises-Fisher distribution (2012)
  • Author(s): Kato, S. and Eguchi, S.
  • Journal Title: arXiv Volume: 1201 Pages: 1-37
  • URL: http://arxiv.org/abs/1201.6476.
• [Journal Article] 円周上のコーシー分布と関連した統計モデル (2012)
  • Author(s): 加藤 昇吾
  • Journal Title: 日本数学会 2012年度 秋季総合分科会 講演アブストラクト Volume: なし Pages: 105-121
  • NAID: 130006026483
• [Journal Article] Projective power entropy and maximum Tsallis entropy distributions (2011)
  • Author(s): S. Eguchi, O. Komori and S. Kato
  • Journal Title: Entropy Volume: 13 Issue: 10 Pages: 1746-1764
  • DOI: 10.3390/e13101746
  • Peer Reviewed
• [Journal Article] A Markov process for circular data (2010)
  • Author(s): Kato, S.
  • Journal Title: Journal of the Royal Statistical Society, Series B (Statistical Methodology) Volume: 72 Issue: 5 Pages: 655-672
  • DOI: 10.1111/j.1467-9868.2010.00748.x
  • Peer Reviewed
• [Presentation] Trigonometric momentによって特徴づけられる円周上の確率分布 (2012)
  • Author(s): 加藤昇吾
  • Organizer: 統計数理セミナー
  • Place of Presentation: 統計数理研究所, 立川
  • Year and Date: 2012-10-10
• [Presentation] 円周上のコーシー分布と関連した統計モデル (2012)
  • Author(s): 加藤昇吾
  • Organizer: 日本数学会 2012年度 秋季総合分科会
  • Place of Presentation: 九州大学, 福岡
  • Year and Date: 2012-09-20
• [Presentation] A family of distributions on the circle with links to, and an application arising from, Mobius transformation (2012)
  • Author(s): 加藤昇吾, Jones, M.C.
  • Organizer: 2012年度 統計関連学会連合大会
  • Place of Presentation: 北海道大学, 札幌
  • Year and Date: 2012-09-11
• [Presentation] Regression analysis of circular data. Workshop on Directional Statistics (2012)
  • Author(s): Kato, S.,
  • Organizer: Satellite Office of the Institute of Statistical Mathematics
  • Place of Presentation: Tokyo,Japan
  • Year and Date: 2012-07-05
• [Presentation] Robust estimation of location and concentration parameters for the von Mises-Fisher distribution (2012)
  • Author(s): Kato, S. and Eguchi, S.
  • Organizer: The 2nd Institute of Mathematical Statistics Asia Pacific Rim Meeting
  • Place of Presentation: Tsukuba University, Tsukuba,Japan
  • Year and Date: 2012-07-04
• [Presentation] A family of circular distributions arising from Brownian motion (2012)
  • Author(s): Kato, S.
  • Organizer: Keio-Yonsei Workshop
  • Place of Presentation: Yokohama,Japan
  • Year and Date: 2012-05-24
• [Presentation] A Mobius transformation induced distribution on the torus (2012)
  • Author(s): Kato, S.
  • Organizer: ISM-ISI-ISSAS Joint Conference 2012
  • Place of Presentation: The Institute of Statistical Mathematics, Tokyo,Japan
  • Year and Date: 2012-02-03
• [Presentation] A Mobius transformation induced distribution on the torus (2012)
  • Author(s): Kato, S.
  • Organizer: ISM-ISI-ISSAS Joint Conference 2012
  • Place of Presentation: 統計数理研究所,立川,日本
  • Year and Date: 2012-02-03
• [Presentation] An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion (2011)
  • Author(s): Kato, S., Jones, M.C.
  • Organizer: International Conference on Advances in Probability and Statistics - Theory and Applications: A Celebration of N. Balakrishnan's 30 Years of Contributions to Statistics
  • Place of Presentation: Chinese University of Hong Kong, Hong Kong, China
  • Year and Date: 2011-12-29
• [Presentation] An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion (2011)
  • Author(s): Kato, S., Jones, M.C.
  • Organizer: International Conference on Advances in Probability and Statistics-Theory and Applications : A Celebration of N.Balakrishnan's 30 Years of Contributions to Statistics
  • Place of Presentation: Chinese University of Hong Kong,香港,中国
  • Year and Date: 2011-12-29
• [Presentation] An extended family of circular distributions related to wrapped Cauchy distributions (2011)
  • Author(s): 加藤昇吾, Jones, M.C.
  • Organizer: 2011年度 統計関連学会連合大会
  • Place of Presentation: 九州大学, 福岡
  • Year and Date: 2011-09-07
• [Presentation] An extended family of circular distributions related to wrapped Cauchy distributions (2011)
  • Author(s): 加藤昇吾, Jones, M.C.
  • Organizer: 2011年度統計関連学会連合大会
  • Place of Presentation: 九州大学,福岡,日本
  • Year and Date: 2011-09-07
• [Presentation] An extension of the wrapped Cauchy distribution via Brownian motion. Complex Phenomena from Statistical Point of View (2011)
  • Author(s): Kato, S.
  • Organizer: Seismology, Environmentology and Economy
  • Place of Presentation: Meiji University, Kawasaki, Japan
  • Year and Date: 2011-09-01
• [Presentation] An extension of the wrapped Cauchy distribution via Brownian motion (2011)
  • Author(s): Kato, S.
  • Organizer: Complex Phenomena from Statistical Point of View～Seismology, Environmentology and Economy～
  • Place of Presentation: 明治大学,川崎,日本(招待講演)
  • Year and Date: 2011-09-01
• [Presentation] 2変量角度データのための確率分布と関連した統計モデル (2011)
  • Author(s): 加藤昇吾
  • Organizer: 統計数理セミナー
  • Place of Presentation: 統計数理研究所, 立川
  • Year and Date: 2011-06-29
• [Presentation] 2変量角度データのための確率分布と関連した統計モデル (2011)
  • Author(s): 加藤昇吾
  • Organizer: 統計数理セミナー
  • Place of Presentation: 統計数理研究所,立川,日本
  • Year and Date: 2011-06-29
• [Presentation] A Markov process for circular data. Seminar on Mathematical Sciences Based on Modeling (2011)
  • Author(s): Kato, S.
  • Organizer: Analysis and Simulation
  • Place of Presentation: Meiji University, Kawasaki, Japan
  • Year and Date: 2011-02-24
• [Presentation] A Markov process for circular data (2011)
  • Author(s): Kato, S.
  • Organizer: Meiji University Global COE Program-Mathematical Sciences Based on Modeling, Analysis and Simulation Seminar
  • Place of Presentation: 明治大学,川崎,日本
  • Year and Date: 2011-02-24
• [Presentation] A distribution for a pair of unit vectors generated by Brownian motion (2011)
  • Author(s): 加藤昇吾
  • Organizer: 今野・梶原研究室セミナ
  • Place of Presentation: 横浜国立大学, 横浜
  • Year and Date: 2011-02-08
• [Presentation] A distribution for a pair of unit vectors generated by Brownian motion (2011)
  • Author(s): 加藤昇吾
  • Organizer: 今野・梶原研究室セミナー
  • Place of Presentation: 横浜国立大学,横浜,日本
  • Year and Date: 2011-02-08
• [Presentation] A family of distributions on the circle with links to Mobius transformation (2010)
  • Author(s): 加藤昇吾, Jones, M.C.
  • Organizer: 日本数学会 2010年度 秋季総合分科会
  • Place of Presentation: 名古屋大学, 名古屋
  • Year and Date: 2010-09-24
• [Presentation] A family of distributions on the circle with links to Mobius transformation (2010)
  • Author(s): 加藤昇吾, Jones, M.C.
  • Organizer: 日本数学会 2010年度 秋季総合分科会
  • Place of Presentation: 名古屋大学,名古屋,日本
  • Year and Date: 2010-09-24
• [Presentation] 角度データの回帰分析 (2010)
  • Author(s): 加藤昇吾
  • Organizer: 統計数理研究所 共同利用研究集会「生物群集の多様性と統計数理」
  • Place of Presentation: 統計数理研究所, 立川
  • Year and Date: 2010-09-14
• [Presentation] 角度データの回帰分析 (2010)
  • Author(s): 加藤昇吾
  • Organizer: 統計数理研究所 共同利用研究集会「生物群集の多様性と統計数理」
  • Place of Presentation: 統計数理研究所,立川,日本
  • Year and Date: 2010-09-14
• [Presentation] 円周上に値をとるマルコフ過程 (2010)
  • Author(s): 加藤昇吾
  • Organizer: 統計数理セミナー
  • Place of Presentation: 統計数理研究所, 立川
  • Year and Date: 2010-05-19
• [Presentation] 円周上に値をとるマルコフ過程 (2010)
  • Author(s): 加藤昇吾
  • Organizer: 統計数理セミナー
  • Place of Presentation: 統計数理研究所,立川,日本
  • Year and Date: 2010-05-19
• [Presentation] A Markov process for circular data (2010)
  • Author(s): 加藤昇吾
  • Organizer: 統計数学セミナー
  • Place of Presentation: 東京大学, 東京
  • Year and Date: 2010-04-28
• [Presentation] A Markov process for circular data (2010)
  • Author(s): 加藤昇吾
  • Organizer: 統計数学セミナー
  • Place of Presentation: 東京大学,東京,日本
  • Year and Date: 2010-04-28
• [Presentation] A family of distributions on the circle with links to, and applications arising from, Mobius transformation (2010)
  • Author(s): Kato, S.
  • Organizer: Two-Day Conference on Statistics and Probability
  • Place of Presentation: Indian Statistical Institute,Kolkata, India
  • Year and Date: 2010-01-22
• [Presentation] A family of distributions on the circle with links to, and applications arising from (2009)
  • Author(s): 加藤昇吾, Jones, M.C.
  • Organizer: Mobius transformation. 科研費研究集会「非対称分布の統計学」
  • Place of Presentation: 慶應義塾大学, 横浜
  • Year and Date: 2009-11-25
• [Presentation] A Markov process for circular time series (2009)
  • Author(s): Kato, S.
  • Organizer: Workshop "Directional, Asymptotic, Differential-Geometric Statistics and Related Area"
  • Place of Presentation: Osaka Prefecture University, Sakai,Japan
  • Year and Date: 2009-11-06
• [Presentation] A family of circular distributions arising from Brownian motion
  • Author(s): Shogo Kato
  • Organizer: Keio-Yonsei Workshop
  • Place of Presentation: Keio University, Yokohama, Japan
• [Presentation] Robust estimation of location and concentration parameters for the von Mises-Fisher distribution
  • Author(s): Shogo Kato and Shinto Eguchi (Shogo Kato)
  • Organizer: The 2nd Institute of Mathematical Statistics Asia Pacific Rim Meeting
  • Place of Presentation: Tsukuba University, Tsukuba, Japan
• [Presentation] Regression analysis of circular data
  • Author(s): Shogo Kato
  • Organizer: Workshop on Directional Statistics
  • Place of Presentation: Satellite Office of the Institute of Statistical Mathematics, Tokyo, Japan
• [Presentation] A family of distributions on the circle with links to, and an application arising from, Mobius transformation
  • Author(s): 加藤 昇吾，M.C. Jones（加藤 昇吾）
  • Organizer: 2012年度 統計関連学会連合大会
  • Place of Presentation: 北海道大学，札幌，日本
  • Invited
• [Presentation] 円周上のコーシー分布と関連した統計モデル
  • Author(s): 加藤 昇吾
  • Organizer: 日本数学会 2012年度 秋季総合分科会
  • Place of Presentation: 九州大学，福岡，日本
  • Invited
• [Presentation] Trigonometric momentによって特徴づけられる円周上の確率分布
  • Author(s): 加藤 昇吾
  • Organizer: 統計数理セミナー
  • Place of Presentation: 統計数理研究所，立川，日本
• [Remarks]
  • URL: http://www.ism.ac.jp/souran/kenkyusya/kato_shogo.html
• [Remarks] Official HP（加藤 昇吾）
  • URL: http://www.ism.ac.jp/souran/kenkyusya/kato_shogo.html
• [Remarks] Personal HP（加藤 昇吾）
  • URL: http://www.ism.ac.jp/~skato/
• [Remarks]
  • URL: http://www.ism.ac.jp/souran/kenkyusya/kato_shogo.html
• [Remarks]
  • URL: http://www.ism.ac.jp/souran/kenkyusya/kato_shogo.html