Two New Relative Efficiencies of Linear Weighted Regression
In statistics parameter theory, usually the
parameter estimations have two kinds, one is the least-square
estimation (LSE), and the other is the best linear unbiased
estimation (BLUE). Due to the determining theorem of
minimum variance unbiased estimator (MVUE), the parameter
estimation of BLUE in linear model is most ideal. But since
the calculations are complicated or the covariance is not
given, people are hardly to get the solution. Therefore, people
prefer to use LSE rather than BLUE. And this substitution
will take some losses. To quantize the losses, many scholars
have presented many kinds of different relative efficiencies in
different views. For the linear weighted regression model, this
paper discusses the relative efficiencies of LSE of β to BLUE
of β. It also defines two new relative efficiencies and gives
their lower bounds.
[1] J.X. Pan. Regression parameters in growth curve model of least squares
estimate and Gauss-Markov theorem.Mathematical statistics and applied
probability. 1988, 3, pp.169-185.
[2] Q.T. Duan, Y.H. Zhang. The relative efficiency of least square estimation
in linear weighted regression. Pure mathematics and applied learning,
1998, 4(3), pp.25-29.
[3] J. Wang, W.X. Wang, C.M. Wang. The relative efficiency of parameter
estimation in linear weighted regression. Guangxi Normal University,
2000, 15(2), pp.37-40.
[4] A.Y. Liu, S.G. Wang. A new relative efficiency of least square estimation
in linear model. Applied probability and statistics, 1989, 15(2), pp.97-104.
[5] P. Bloomfield, G.S. Watson. The relative efficiency of least square
estimation. Biometrika, 1975, 62, pp.121-128. [6] X.X. Chen. A new relative efficiency of parameter estimation in linear
model. Jiangxi Normal University, 1999, 23(4), pp.313-315.
[7] B.G. Tian, N. Chen. The relative efficiency of parameter estimation in
linear weighted regression. World Academy of Science, Engineering and
Technology, 2014, 8(11), pp.1348-1351.
[8] Y.L. Huan, G.J. Chen. The relative efficiency of parameter estimation in
linear model. Applied probability and statistics, 1998, 14(2), pp.159-164.
[9] X.M. Liu, J.Zhang. A new relative efficiency of parameter estimation in
linear model. Mathematical theory and application, 2000, 20(3), pp.26-29.
[10] J.L. Wang, D.D. Gao. The relative efficiency of Generalized least square
estimation under euclidean norm. Applied probability and statistics,
1991, 7(4), pp.361-366.
[11] H.S. Liu, R.Q. Li. The Relative Efficiency of the Parameter Estimate
in Linear Weighted Regression. Journal of Taiyuan University of
Technology, 2005, 36, pp.612-614.
[12] L. Xia, B.G. Tian, N.N. Wang. The Relative Efficiency of Linear
Weighted Regression. Science-technology and engineering, 2009, 20(10),
pp.6139-6141.
[13] J. Li, L. Xia, N.N. Wang. A new relative efficiency in generalized linear
model. Proceedings of the Eighth International Conference on Matrix
Theory and its Applications. 2009, pp.84-86.
[14] S.G. Wang, M.X. Wu, Z.Z. Jia. Matrix inequlity. Beijing Science Press,
2006.
[15] C.G. Khatri, C.R. Rao. Some generalization of Kantorovich inequality.
Sankhya, 1982, 44, pp.91-102.
[16] S.G. Wang. The theory and application of linear model. Anhui
Education Press, 1987.
[17] X.R. Chen. Statistics introduction. Beijing Science Press, 1981,
pp.104-108.
[1] J.X. Pan. Regression parameters in growth curve model of least squares
estimate and Gauss-Markov theorem.Mathematical statistics and applied
probability. 1988, 3, pp.169-185.
[2] Q.T. Duan, Y.H. Zhang. The relative efficiency of least square estimation
in linear weighted regression. Pure mathematics and applied learning,
1998, 4(3), pp.25-29.
[3] J. Wang, W.X. Wang, C.M. Wang. The relative efficiency of parameter
estimation in linear weighted regression. Guangxi Normal University,
2000, 15(2), pp.37-40.
[4] A.Y. Liu, S.G. Wang. A new relative efficiency of least square estimation
in linear model. Applied probability and statistics, 1989, 15(2), pp.97-104.
[5] P. Bloomfield, G.S. Watson. The relative efficiency of least square
estimation. Biometrika, 1975, 62, pp.121-128. [6] X.X. Chen. A new relative efficiency of parameter estimation in linear
model. Jiangxi Normal University, 1999, 23(4), pp.313-315.
[7] B.G. Tian, N. Chen. The relative efficiency of parameter estimation in
linear weighted regression. World Academy of Science, Engineering and
Technology, 2014, 8(11), pp.1348-1351.
[8] Y.L. Huan, G.J. Chen. The relative efficiency of parameter estimation in
linear model. Applied probability and statistics, 1998, 14(2), pp.159-164.
[9] X.M. Liu, J.Zhang. A new relative efficiency of parameter estimation in
linear model. Mathematical theory and application, 2000, 20(3), pp.26-29.
[10] J.L. Wang, D.D. Gao. The relative efficiency of Generalized least square
estimation under euclidean norm. Applied probability and statistics,
1991, 7(4), pp.361-366.
[11] H.S. Liu, R.Q. Li. The Relative Efficiency of the Parameter Estimate
in Linear Weighted Regression. Journal of Taiyuan University of
Technology, 2005, 36, pp.612-614.
[12] L. Xia, B.G. Tian, N.N. Wang. The Relative Efficiency of Linear
Weighted Regression. Science-technology and engineering, 2009, 20(10),
pp.6139-6141.
[13] J. Li, L. Xia, N.N. Wang. A new relative efficiency in generalized linear
model. Proceedings of the Eighth International Conference on Matrix
Theory and its Applications. 2009, pp.84-86.
[14] S.G. Wang, M.X. Wu, Z.Z. Jia. Matrix inequlity. Beijing Science Press,
2006.
[15] C.G. Khatri, C.R. Rao. Some generalization of Kantorovich inequality.
Sankhya, 1982, 44, pp.91-102.
[16] S.G. Wang. The theory and application of linear model. Anhui
Education Press, 1987.
[17] X.R. Chen. Statistics introduction. Beijing Science Press, 1981,
pp.104-108.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:70114", author = "Shuimiao Wan and Chao Yuan and Baoguang Tian", title = "Two New Relative Efficiencies of Linear Weighted Regression", abstract = "In statistics parameter theory, usually the
parameter estimations have two kinds, one is the least-square
estimation (LSE), and the other is the best linear unbiased
estimation (BLUE). Due to the determining theorem of
minimum variance unbiased estimator (MVUE), the parameter
estimation of BLUE in linear model is most ideal. But since
the calculations are complicated or the covariance is not
given, people are hardly to get the solution. Therefore, people
prefer to use LSE rather than BLUE. And this substitution
will take some losses. To quantize the losses, many scholars
have presented many kinds of different relative efficiencies in
different views. For the linear weighted regression model, this
paper discusses the relative efficiencies of LSE of β to BLUE
of β. It also defines two new relative efficiencies and gives
their lower bounds.", keywords = "Linear weighted regression, Relative efficiency,
Lower bound, Parameter estimation.", volume = "9", number = "6", pages = "305-4", }