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Akio Namba - One of the best experts on this subject based on the ideXlab platform.
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mse performance of the weighted average estimators consisting of shrinkage estimators when each Individual Regression Coefficient is estimated
Communications in Statistics-theory and Methods, 2019Co-Authors: Haifeng Xu, Akio NambaAbstract:AbstractIn this paper, we analytically derive the exact formula for the mean squared error (MSE) of two weighted average (WA) estimators for each Individual Regression Coefficient. Further, we execute numerical evaluations to investigate small sample properties of the WA estimators, and compare the MSE performance of the WA estimators with the other shrinkage estimators and the usual OLS estimator. Our numerical results show that (1) the WA estimators have smaller MSE than the other shrinkage estimators and the OLS estimator over a wide region of parameter space; (2) the range where the relative MSE of the WA estimator is smaller than that of the OLS estimator gets narrower as the number of explanatory variables k increases.
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mse performance of the weighted average estimators consisting of shrinkage estimators when each Individual Regression Coefficient is estimated
Communications in Statistics-theory and Methods, 2019Co-Authors: Akio NambaAbstract:In this paper, we analytically derive the exact formula for the mean squared error (MSE) of two weighted average (WA) estimators for each Individual Regression Coefficient. Further, we execute nume...
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a sufficient condition for the mse dominance of the positive part shrinkage estimator when each Individual Regression Coefficient is estimated in a misspecified linear Regression model
Journal of Statistical Computation and Simulation, 2018Co-Authors: Akio Namba, Haifeng XuAbstract:ABSTRACTIn this paper, assuming that there exist omitted explanatory variables in the specified model, we derive the exact formula for the mean squared error (MSE) of a general family of shrinkage ...
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mse dominance of the positive part shrinkage estimator when each Individual Regression Coefficient is estimated
Statistical Papers, 2015Co-Authors: Akio NambaAbstract:In this paper we consider a Regression model and a general family of shrinkage estimators of Regression Coefficients. The estimation of each Individual Regression Coefficient is important in some practical situations. Thus, we derive the formula for the mean squared error (MSE) of the general class of shrinkage estimators for each Individual Regression Coefficient. It is shown analytically that the general family of shrinkage estimators is dominated by its positive-part variant in terms of MSE whenever there exists the positive-part variant or, in other words, the shrinkage factor can be negative for some parameter and data values. Copyright Springer-Verlag Berlin Heidelberg 2015
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mse dominance of the positive part shrinkage estimator when each Individual Regression Coefficient is estimated
Statistical Papers, 2015Co-Authors: Akio NambaAbstract:In this paper we consider a Regression model and a general family of shrinkage estimators of Regression Coefficients. The estimation of each Individual Regression Coefficient is important in some practical situations. Thus, we derive the formula for the mean squared error (MSE) of the general class of shrinkage estimators for each Individual Regression Coefficient. It is shown analytically that the general family of shrinkage estimators is dominated by its positive-part variant in terms of MSE whenever there exists the positive-part variant or, in other words, the shrinkage factor can be negative for some parameter and data values.
Haifeng Xu - One of the best experts on this subject based on the ideXlab platform.
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mse performance of the weighted average estimators consisting of shrinkage estimators when each Individual Regression Coefficient is estimated
Communications in Statistics-theory and Methods, 2019Co-Authors: Haifeng Xu, Akio NambaAbstract:AbstractIn this paper, we analytically derive the exact formula for the mean squared error (MSE) of two weighted average (WA) estimators for each Individual Regression Coefficient. Further, we execute numerical evaluations to investigate small sample properties of the WA estimators, and compare the MSE performance of the WA estimators with the other shrinkage estimators and the usual OLS estimator. Our numerical results show that (1) the WA estimators have smaller MSE than the other shrinkage estimators and the OLS estimator over a wide region of parameter space; (2) the range where the relative MSE of the WA estimator is smaller than that of the OLS estimator gets narrower as the number of explanatory variables k increases.
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a sufficient condition for the mse dominance of the positive part shrinkage estimator when each Individual Regression Coefficient is estimated in a misspecified linear Regression model
Journal of Statistical Computation and Simulation, 2018Co-Authors: Akio Namba, Haifeng XuAbstract:ABSTRACTIn this paper, assuming that there exist omitted explanatory variables in the specified model, we derive the exact formula for the mean squared error (MSE) of a general family of shrinkage ...
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finite sample properties of an hpt estimator when each Individual Regression Coefficient is estimated in a misspecified linear Regression model
Communications in Statistics-theory and Methods, 2016Co-Authors: Haifeng XuAbstract:ABSTRACTIn this paper, assuming that there exist omitted variables in the specified model, we analytically derive the exact formula for the mean squared error (MSE) of a heterogeneous pre-test (HPT) estimator whose components are the ordinary least squares (OLS) and feasible ridge Regression (FRR) estimators. Since we cannot examine the MSE performance analytically, we execute numerical evaluations to investigate small sample properties of the HPT estimator, and compare the MSE performance of the HPT estimator with those of the FRR estimator and the usual OLS estimator. Our numerical results show that (1) the HPT estimator is more efficient when the model misspecification is severe; (2) the HPT estimator with the optimal critical value obtained under the correctly specified model can be safely used even when there exist omitted variables in the specified model.
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mse performance and minimax regret significance points for a hpt estimator when each Individual Regression Coefficient is estimated
Communications in Statistics-theory and Methods, 2013Co-Authors: Haifeng XuAbstract:In this article, we consider a heterogeneous preliminary test (HPT) estimator whose components are the OLS and feasible ridge Regression (FRR) estimators, and derive the exact formulae for the moments of the HPT estimator using mathematical method. Since we cannot examine the MSE of the HPT estimator analytically, we execute the numerical evaluation to investigate the MSE performance of the HPT estimator, and compare the MSE performance of the HPT estimator with those of the FRR estimator and the usual OLS estimator. Furthermore, using the minimax regret criterion proposed by Sawa and Hiromatsu (1973), we derive the optimal critical points of the preliminary F test. Our results show that the optimal significance points are greater than 19% and the optimal signicance points decrease as the denominator degrees of freedom of the preliminary F test statistic increases.
Kazuhiro Ohtani - One of the best experts on this subject based on the ideXlab platform.
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risk performance of a pre test ridge Regression estimator under the linex loss function when each Individual Regression Coefficient is estimated
Journal of Statistical Computation and Simulation, 2010Co-Authors: Akio Namba, Kazuhiro OhtaniAbstract:In this paper, we consider a linear Regression model and propose a pre-test ridge Regression estimator which is obtained by incorporating a pre-test into a ridge Regression estimator proposed by Huang [J.-C. Huang, Improving the estimation precision for a selected parameter in multiple Regression analysis: An algebraic approach, Econ. Lett. 62 (1999), pp. 261–264]. We derive the exact formula for the risk of the estimator under the asymmetric LINEX loss function. Our numerical results show that the risk performance of the estimator is improved by incorporating the pre-test.
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improving the stein rule estimator of each Individual Regression Coefficient using the stein varience estimator
1998Co-Authors: Kazuhiro OhtaniAbstract:A substantial body of literature on Regression has focused on estimators which are biased but more precise than the ordinary least squares (OLS) estimator. As is discussed in Paelinck and Klaasseen (1979), estimation of Regression parameters is important in spatial econometric models, and the precision of estimation is often measured by the mean square error (MSE). It is well known that when three or more Coefficients are estimated simultaneously, the Stein-rule (SR) estimator proposed by Stein (1955) and James and Stein (1961) dominates the OLS estimator in terms of MSE. [Exactly speaking, in terms of predictive MSE.] Further, the positive-part Stein-rule (PSR) estimator dominates the SR estimator in terms of MSE. [See, for example, Judge and Yancey (1986).
一博 大谷 - One of the best experts on this subject based on the ideXlab platform.
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small sample properties of a pre test stein rule estimator for each Individual Regression Coefficient under an alternative null hypothesis in the pre test
Kobe University economic review, 2012Co-Authors: 明生 難波, 一博 大谷Abstract:In this paper we consider a pre-test Stein-rule (SR) estimator for each Individual Regression Coefficient when the null hypothesis in the pre-test is that the Regression Coefficient to be estimated is a zero. We derive the explicit formula for the MSE of the pre-test SR estimator, and examine the MSE performance of the pre-test SR estimator by numerical evaluations. Our numerical results show that using the null hypothesis that all the Regression Coefficients are zeros yields a better MSE performance than using the null hypothesis that the Regression Coefficient to be estimated is a zero.
明生 難波 - One of the best experts on this subject based on the ideXlab platform.
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small sample properties of a pre test stein rule estimator for each Individual Regression Coefficient under an alternative null hypothesis in the pre test
Kobe University economic review, 2012Co-Authors: 明生 難波, 一博 大谷Abstract:In this paper we consider a pre-test Stein-rule (SR) estimator for each Individual Regression Coefficient when the null hypothesis in the pre-test is that the Regression Coefficient to be estimated is a zero. We derive the explicit formula for the MSE of the pre-test SR estimator, and examine the MSE performance of the pre-test SR estimator by numerical evaluations. Our numerical results show that using the null hypothesis that all the Regression Coefficients are zeros yields a better MSE performance than using the null hypothesis that the Regression Coefficient to be estimated is a zero.