Two New Relative Efficiencies of Linear Weighted Regression

Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1106981

References:

[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.