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A study on statistical theory of choosing a smoothing parameter for spectral density estimation and its application

Research Project

Project/Area Number 20500248
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Statistical science
Research InstitutionHokkaido University

Principal Investigator

KAKIZAWA Yoshihide  Hokkaido University, 大学院・経済学研究科, 准教授 (30281778)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords定常過程 / スペクトル密度 / ノンパラメトリック推定 / カーネル密度推定
Research Abstract

The smoothing parameter in nonparametric function estimation plays a role in controlling the trade off between the approximation error (in terminology of Statistics, it is nothing but bias of the estimator) and variance of the estimator. In this research, I discussed a new spectral density estimator/probability density estimator based on a generalized Bernstein polynomial approximation theory, in which the degree of polynomial and the additional second parameter are the smoothing parameters. Especially, main focus is the selection problem of these two parameters, where the latter second parameter enables us to generalize the classical Bernstein method. I established several formulas of asymptotic bias, variance and mean squared error as well as the asymptotic normality of the proposal.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (7 results)

All 2011 2010 2009

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (5 results)

  • [Journal Article] A note on generalized Bernstein polynomial density estimators.2011

    • Author(s)
      Kakizawa, Y.
    • Journal Title

      Statistical Methodology. 8(2)

      Pages: 136-153

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on generalized Bernstein polynomial density estimators2011

    • Author(s)
      Yoshihide KAKIZAWA
    • Journal Title

      Statistical Methodology

      Volume: 8(2) Pages: 136-153

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] A generalized Bernstein polynomial approach to density estimation.2010

    • Author(s)
      柿沢佳秀
    • Organizer
      研究集会「統計的推測方法の理論的展開とその応用」
    • Place of Presentation
      熊本大学(熊本)
    • Year and Date
      2010-11-18
    • Related Report
      2010 Final Research Report
  • [Presentation] ベルンシュタイン多項式による密度推定について2010

    • Author(s)
      柿沢佳秀
    • Organizer
      応用統計ワークショップ
    • Place of Presentation
      東京大学(東京)
    • Year and Date
      2010-05-21
    • Related Report
      2010 Final Research Report
  • [Presentation] Generalized Bernstein polynomial density estimation.2010

    • Author(s)
      柿沢佳秀
    • Organizer
      研究集会「第12回ノンパラメトリック統計解析とベイズ統計」
    • Place of Presentation
      慶応大学(東京)
    • Year and Date
      2010-03-29
    • Related Report
      2010 Final Research Report
  • [Presentation] On generalized Bernstein polynomial density estimators.2009

    • Author(s)
      柿沢佳秀
    • Organizer
      日本数学会2009年度秋季総合分科会
    • Place of Presentation
      大阪大学(大阪)
    • Year and Date
      2009-09-26
    • Related Report
      2010 Final Research Report
  • [Presentation] On generalized Bernstein polynomial density estimators2009

    • Author(s)
      柿沢佳秀
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-26
    • Related Report
      2009 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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