Evaluation of precision of estimation of shrinkage estimators by the bootstrap method, and its applications to empirical researches
Project/Area Number 
13630032

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Economic statistics

Research Institution  Kobe 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)

Keywords  shrinkage estimators / bootstrap method / pretest / coefficient of determination / small sample properties / estimator for error variance / Steinrule 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 SteinRule (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 pretest for linear restrictions on regression coefficients. We derived the exact formula for the moments of the pretest estimator for the coefficient of determination and compare the bias and MSE of the pretest estimator for the coefficient of determination with those of the usual estimator. Our numerical results show that although the bias of the pretest 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 pretest. Now, we are developing the procedure of the bootstrap method. 3. We derived the exact distribution of the pretest estimator for the regression error variance, and examined the small sample properties of the pretest estimator. Now, we are developing the procedure of the bootstrap method. Less

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