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Evaluation of precision of estimation of shrinkage estimators by the bootstrap method, and its applications to empirical researches

Research Project

Project/Area Number 13630032
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Economic statistics
Research InstitutionKobe University

Principal Investigator

OHTANI Kazuhiro  Kobe University, Graduate School of Economics, Professor, 経済学研究科, 教授 (00106626)

Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2002: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2001: ¥800,000 (Direct Cost: ¥800,000)
Keywordsshrinkage estimators / bootstrap method / pre-test / coefficient of determination / small sample properties / estimator for error variance / Stein-rule estimator / 決定係数 / 誤差分散推定量 / 予備検定推定量
Research Abstract

1. The coefficient of determination is usually by using the ordinary least squares (OLS) estimator. In this research, we dealt with the coefficient of determination defined by using the Stein-Rule (SR) estimator. Although we derived the exact formula for the moments of the coefficient of determination based on the SR estimator, the formula for the moments is very complicated and it depends on unknown parameters. When the formula for the moments of estimators is very complicated and it depends on unknown parameter, it is very difficult to evaluate the precision of estimation. However, if we use the bootstrap method proposed by Efron (1979), it is possible to evaluate the precision of estimation. Thus, we considered how we apply the bootstrap method to estimating the precision of estimation and the confidence interval of the coefficient of determination based on the SR estimator. We also generated the empirical estimates of the precision of estimation by Monte Carlo experiments, and comp … More ared them with the precision of estimation evaluated by the exact formula. The Monte Carlo results showed that the bootstrap method worked effectively.
2. In this research, we examined the small sample properties of the coefficient of determination when a model is selected by a pre-test for linear restrictions on regression coefficients. We derived the exact formula for the moments of the pre-test estimator for the coefficient of determination and compare the bias and MSE of the pre-test estimator for the coefficient of determination with those of the usual estimator. Our numerical results show that although the bias of the pre-test estimator for he coefficient of determination is smaller than that of the usual coefficient of determination, the MSE performance depends on the size of the pre-test. Now, we are developing the procedure of the bootstrap method.
3. We derived the exact distribution of the pre-test estimator for the regression error variance, and examined the small sample properties of the pre-test estimator. Now, we are developing the procedure of the bootstrap method. Less

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (9 results)

All Other

All Publications (9 results)

  • [Publications] Ohtani, Kazuhiro: "Exact Distribution of a Pre-Test Estimator for Regression Error Variance when there are Omitted Variables"Statistics and Probability Letters. 60・2. 129-140 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Ohtani, Kazuhiro: "Small Sample Properties of R-Squared When a Pre-Test for Linear Restrictions on Regression Coefficients is conducted"Kobe University Economic Review. 48. 29-39 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 大谷 一博: "Stein型推定量に基づく決定係数のブートストラップ法による精度評価"国民経済雑誌. 187・5(近刊). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kazuhiro Ohtani: "Exact Distribution of a Pre-Test Estimator for Regression Error Variance when there are Omitted Variables"Statistics and Probability Letters. 60-2. 129-140 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kazuhiro Ohtani: "Small Sample Properties of R-Squared When a Pre-Test for Linear Restrictions on Regression Coefficients is conducted"Kobe University Economic Review. 48. 29-39 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kazuhiro Ohtani: "Evaluating the precision of the coefficient of determination based on the Stein-rule estimator by the bootstrap method"Kokumin Keizai Zasshi. 187-5, forthcoming. (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Ohtani, Kazuhiro: "Exact Distribution of a Pre-Test Estimator for Regression Error Variance when there are Omitted Variables"Statistics and Probability Letters. 60・2. 129-140 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Ohtani, Kazuhiro: "Small Sample Properties of R-Squared When a Pre-Test for Linear Restrictions on Regression Coefficients is conducted"Kobe University Economic Review. 48. (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 大谷 一博: "Stein型推定量に基づく決定係数のブートストラップ法による精度評価"国民経済雑誌. 187・5(近刊). (2003)

    • Related Report
      2002 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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