The New Relative Efficiency Based on the Least Eigenvalue in Generalized Linear Model

A new relative efficiency is defined as LSE and BLUE in the generalized linear model. The relative efficiency is based on the ratio of the least eigenvalues. In this paper, we discuss about its lower bound and the relationship between it and generalized relative coefficient. Finally, this paper proves that the new estimation is better under Stein function and special condition in some degree.

Authors:

• Chao Yuan
• Bao Guang Tian

Keywords:

• Generalized linear model
• generalized relative coefficient
• least eigenvalue
• relative efficiency.

References:

[1] 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.
[2] Rao. C.R. Least squares theory using an estimated dispersion matrix and its application to measurement of signals,In Proceedings of the Fifth Berkeley Symposium on Math. Statist &Pro.Eds.by Lecam, J and Neyman, J . Vol.1.1967.
[3] Knott On the Minimum efficiency of least Squaces.Biometrika,1975,62, pp.129-132.
[4] 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.
[5] S.G. Wang, M.X. Wu, Z.Z. Jia. Matrix inequality. Beijing Science Press,2006.
[6] R.T. Zhang, K.T. Fang. An introduction to multivariate statistical analysis. Beijing Science Press,1999.
[7] A.J. Shi. Relative efficiency based on the minimum eigenvalue. Journal of Nanjing University of Posts and Telecommunications, 2007, 27(2),pp.76-79.