NAMBA Akio | |

Graduate School of Economics / Division of Economics | |

Professor | |

Business / Economics |

Last Updated :2022/01/10

#### ＜Faculty / Graduate School / Others＞

Graduate School of Economics / Division of Economics#### ＜Related Faculty / Graduate School / Others＞

Faculty of Economics / Department of Economics, Center for Mathematical and Data Sciences

- Faculty of Economics, 2020, SeminarⅠ
- Faculty of Economics, 2020, Seminar
- Faculty of Economics, 2020, Economics Readings in English
- Faculty of Economics, 2020, Statistics
- Faculty of Economics, 2020, Advanced Liberal Arts Seminar in Economics (Seminar B)
- Graduate School of Economics, 2020, Econometrics A
- Graduate School of Economics, 2020, Seminar
- Graduate School of Economics, 2020, Research on a Special Problem in Economics
- Graduate School of Economics, 2020, Seminar

- Lead, Feb. 2020, 国民経済雑誌, 221 (2), 73 - 84, Japanese
**Simulation Studies on the Approximation of the Distributions of the Stein-Rule Estimators by Asymptotic and Bootstrap Methods**Scientific journal

In this paper, we consider a regression model and propose estimators which are the weighted averages of two estimators among three estimators the Stein-rule (SR), the minimum mean squared error (MMSE), and the adjusted minimum mean-squared error (AMMSE) estimators. It is shown that one of the proposed estimators has smaller mean-squared error (MSE) than the positive-part Stein-rule (PSR) estimator over a moderate region of parameter space when the number of the regression coefficients is small (i.e., 3), and its MSE performance is comparable to the PSR estimator even when the number of the regression coefficients is not so small.

Taylor and Francis Inc., 04 Mar. 2018, Communications in Statistics - Theory and Methods, 47 (5), 1204 - 1214, English[Refereed]

Scientific journal

- The Keizai-keiei Gakkai, Kobe University, Feb. 2018, Kokumin-keizai Zasshi, 217 (2), Japanese
**A Study on an Application of the Stein-Rule Estimator in a Linear Regression Model with a Structural Break**Scientific journal

- Taylor and Francis, 2018, Journal of Statistical Computation and Simulation, English
**PMSE dominance of the positive-part shrinkage estimator in a regression model with proxy variables**[Refereed]

Scientific journal

- 2018, Communications in Statistics - Theory and Methods, English
**MSE performance of the weighted average estimators consisting of shrinkage estimators when each individual regression coefficient is estimated**[Refereed]

Scientific journal

- Taylor and Francis, 2018, Journal of Statistical Computation and Simulation, English
**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**[Refereed]

Scientific journal

In this article, we consider the Wald test statistic for testing equality between the sets of regression coefficients in two linear regression models when the disturbance variances may possibly be unequal. This test can be also used as a test for a structural break. However, it is well known that the test based on the Wald test statistic suffers from severe size distortion in small sample when the disturbance variances of the two regression models are unequal. Our simulation results show that substantial improvements are made when the bootstrap methods are applied.

TAYLOR & FRANCIS INC, 2017, COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 46 (5), 4127 - 4139, English[Refereed]

Scientific journal

- 神戸大学経済経営学会, 2016, 国民経済雑誌, 213 (2), 63 - 75, Japanese
**Simulation Analysis of a Wild Bootstrap Test for the Mean**Research institution

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.

SPRINGER, May 2015, STATISTICAL PAPERS, 56 (2), 379 - 390, English[Refereed]

Scientific journal

- 2014, Kobe University Economic Review, English
**Double Bootstrap Test for a Structural Break when the Disturbance Variance Changes with the Break**Research institution

- 2013, 国民経済雑誌, Japanese
**Simulation Comparison of the Double Bootstrap and the Fast Double Bootstrap Tests**Research institution

- Apr. 2012, 国民経済雑誌, 第205巻3号41-55, Japanese
**平均に対する平滑化ブートストラップ法におけるバンド幅の選択に関する一考察**Scientific journal

- Apr. 2012, Kobe University Economic Review, (58), 1 - 9, English
**Small Sample Properties of a Pre-Test Stein-Rule Estimator for Each Individual Regression Coefficient under an Alternative Null Hypothesis in the Pre-Test**Scientific journal

- Apr. 2012, Communications in Statistics—Theory and Methods, Vol 41, No 9, pp. 1692-1700, English
**MSE Performance of a Heterogeneous Pre-Test Ridge Regression Estimator**[Refereed]

Scientific journal

- 2012, Communications in Statistics-Theory and Methods, Vol. 41, pp.1692-1700, English
**MSE performance of a heterogeneous pre-test ridge regression estimator**[Refereed]

Scientific journal

- 2010, Journal of Statistical Computation and Simulation, 80・255-262, English
**Risk Performance of a Pre-test Ridge Regression Estimator under the LINEX Loss Function when Each Individual Regression Coefficient is Estimated**[Refereed]

Scientific journal

In this paper we consider a linear regression model with omitted relevant regressors and multivariatet error terms. The explicit formula for the Pitman nearness criterion of the Stein-rule (SR) estimator relative to the ordinary least squares (OLS) estimator is derived. It is shown numerically that the dominance of the SR estimator over the OLS estimator under the Pitman nearness criterion can be extended to the case of the multivariatet error distribution when the specification error is not severe. It is also shown that the dominance of the SR estimator over the OLS estimator cannot be extended to the case of the multivariatet error distribution when the specification error is severe. © Springer-Verlag 2006.

Jan. 2007, Statistical Papers, 48 (1), 151 - 162, English[Refereed]

Scientific journal

**Risk comparison of the Stein-rule estimator in a linear regression model with omitted relevant regressors and multivariate t errors under the Pitman nearness criterion**in this paper we consider a linear regression model with omitted relevant regressors and multivariate t error terms. The explicit formula for the Pitman nearness criterion of the Stein-rule (SR) estimator relative to the ordinary least squares (OLS) estimator is derived. It is shown numerically that the dominance of the SR estimator over the OLS estimator under the Pitman nearness criterion can be extended to the case of the multivariate t error distribution when the specification error is not severe. It is also shown that the dominance of the SR estimator over the OLS estimator cannot be extended to the case of the multivariate t error distribution when the specification error is severe.

SPRINGER, Jan. 2007, STATISTICAL PAPERS, 48 (1), 151 - 162, English[Refereed]

Scientific journal

Consider a linear regression model with some relevant regressors are unobservable. In such a situation, we estimate the model by using the proxy variables as regressors or by simply omitting the relevant regressors. In this paper, we derive the explicit formula of the predictive mean squared error (PMSE) of the Stein-rule (SR) estimator and the positive-part Stein-rule (PSR) estimator for the regression coefficients when the proxy variables are used. We examine the effect of using the proxy variables on the risk performances of the SR and PSR estimators. It is shown analytically that the PSR estimator dominates the SR estimator even when the proxy variables are used. Also, our numerical results show that using the proxy variables is preferable to omitting the relevant regressors. (C) 2005 Elsevier B.V. All rights reserved.

ELSEVIER SCIENCE BV, May 2006, STATISTICS & PROBABILITY LETTERS, 76 (9), 898 - 906, English[Refereed]

Scientific journal

- Jan. 2005, 国民経済雑誌, 191巻 (第1号), 89 - 96, Japanese
**スタイン型推定量の平均自乗誤差に関するパラドックス**Scientific journal

- Sep. 2004, 国民経済雑誌, 190巻 (3号), 89 - 100, Japanese
**シミュレーションによる疑似最尤法および経験尤度に基づく方法の比較**Scientific journal

In this paper we consider to test the hypothesis using the empirical likelihood. To calculate the critical value of the test, two bootstrap methods are applied. Our simulation results indicate that the bootstrap methods improve the small sample property of the test.

MARCEL DEKKER INC, 2004, COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 33 (1), 99 - 108, English[Refereed]

Scientific journal

In this paper, we consider a regression model with omitted relevant regressors and a general family of shrinkage estimators of regression coefficients. We derive the formula for the predictive mean squared error (PMSE) of the estimators. It is shown analytically that the positive-part shrinkage estimator dominates the ordinary shrinkage estimator even when there are omitted relevant regressors. Also, as an example, our result is applied to the double k-class estimator. (C) 2003 Elsevier Science B.V. All rights reserved.

ELSEVIER SCIENCE BV, Jul. 2003, STATISTICS & PROBABILITY LETTERS, 63 (4), 375 - 385, English[Refereed]

Scientific journal

In this paper, using the asymmetric LINEX loss function we derive and numerically evaluate the risk function of the new feasible ridge regression estimator. We also examine the risk performance of this estimator when the LINEX loss function is used.

TAYLOR & FRANCIS LTD, Apr. 2003, JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 73 (4), 303 - 310, English[Refereed]

Scientific journal

In this paper we consider the double k-class estimator which incorporates the Stein variance estimator. This estimator is called the SVKK estimator. We derive the explicit formula for the mean squared error (MSE) of the SVKK estimator for each individual regression coefficient. It is shown analytically that the MSE performance of the Stein-rule estimator for each individual regression coefficient can be improved by utilizing the Stein variance estimator. Also, MSE's of several estimators included in a family of the SVKK estimators are compared by numerical evaluations.

SPRINGER-VERLAG, Jan. 2003, STATISTICAL PAPERS, 44 (1), 117 - 124, English[Refereed]

Scientific journal

**MSE dominance of the PT-2SHI estimator over the positive-part Stein-rule estimator in regression**In this paper, we consider a heterogeneous pre-test estimator which consists of the two-stage hierarchial information (2SHI) estimator and the Stein-rule (SR) estimator. This estimator is called the pre-test 2SHI (PT-2SHI) estimator. It is shown analytically that the PT-2SHI estimator dominates the SR estimator in terms of mean squared error (MSE) if the parameter values in the PT-2SHI estimator are chosen appropriately. Moreover, our numerical results show that the appropriate PT-2SHI estimator dominates the positive-part Stein-rule (PSR) estimator. (C) 2000 Elsevier Science B.V. All rights reserved.

ELSEVIER SCIENCE BV, Aug. 2000, JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 89 (1-2), 175 - 185, English[Refereed]

Scientific journal

- Ecosta 2017, Jun. 2017, English, The Hong Kong University of Science and Technology, International conference
**MSE performance of the weighted average estimators consisting of shrinkage estimators**[Invited]

Invited oral presentation

- Econometric Seminar, Oct. 2016, English, University of California-Riverside, International conference
**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**Oral presentation

- The 1st Annual International Conference on Applied Econometrics in Hawaii, Nov. 2015, English, Ala Moana Hotel, Hawaii, International conference
**Simulations on the Wild Bootstrap Tests for a Structural Break when the Break Point is Unknown and the Variance Changes with the Break**Oral presentation

- 学術研究助成基金助成金／基盤研究(C), Apr. 2018 - Mar. 2023, Principal investigator
Competitive research funding

- 学術研究助成基金助成金／若手研究(B), Apr. 2014 - Mar. 2018, Principal investigator
Competitive research funding

- 科学研究費補助金／基盤研究(A), 2011
Competitive research funding

- 科学研究費補助金／若手研究(B), 2006, Principal investigator
Competitive research funding