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

Bootstrap法收缩估计器估计精度评价及其在实证研究中的应用

• 批准号: 13630032
• 负责人: OHTANI Kazuhiro
• 金额: $ 0.83万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13630032/
• 关键词: shrinkage 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

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

1. 确定系数通常采用普通最小二乘（OLS）估计。在本研究中，我们处理由Stein-Rule （SR）估计量定义的确定系数。虽然我们在SR估计的基础上推导出了确定系数矩的精确公式，但矩的公式非常复杂，并且依赖于未知参数。当估计量的矩量公式非常复杂且依赖于未知参数时，很难对估计精度进行评估。然而，如果我们使用Efron（1979）提出的bootstrap方法，则可以评估估计的精度。因此，我们考虑如何应用自举法来估计估计的精度和基于SR估计量的确定系数的置信区间。通过蒙特卡罗实验对估计精度进行了经验估计，并与精确公式估计的估计精度进行了比较。蒙特卡洛结果表明，自举法是有效的。在这项研究中，我们检查了小样本性质的决定系数，当一个模型是通过对回归系数的线性限制的预测试选择。我们推导了决定系数的预测试估计量的矩的精确公式，并将决定系数的预测试估计量的偏差和MSE与通常估计量的偏差和MSE进行了比较。我们的数值结果表明，虽然预检验估计器对决定系数的偏差小于通常的决定系数，但MSE的性能取决于预检验的大小。现在，我们正在开发自举法的程序。我们推导了回归误差方差的预检验估计量的精确分布，并检验了预检验估计量的小样本性质。现在，我们正在开发自举法的程序。少

项目成果

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)

Kazuhiro Ohtani：“当存在遗漏变量时回归误差方差的预测试估计量的精确分布”统计和概率字母。

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)

Ohtani, Kazuhiro：“对回归系数的线性限制进行预测试时 R 平方的小样本属性”神户大学经济评论。