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Abstract

This paper deals with the efficiencies of the least square estimates in linear models. For the Gauss-Markov model, a new efficiency is proposed and its lower bounds are given. For the linear model with variance components, an efficiency is introduced and its lower bounds, which are independent of unknown parameters, are obtained.

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References

  • BAKSALARY, J. K. (1980), A new bound for the euclidian norm of the difference between the least squares and the best linear unbiased estimators, Ann. 8: 679–681.

    Article  Google Scholar 

  • BAKSALARY, J. K., Kala, R. (1978), A bound for the euclidian norm of the difference between the least squares and the best linear unbiased estimates, Ann. Statist., 6: 1390–1393.

    Article  Google Scholar 

  • BLOOMFIELD, P., WASTON, G. S. (1975), The inefficiency of least squares, Biometrika, 62: 121–128.

    Article  Google Scholar 

  • CHEN, J. B., CHEN, T. (1991), The error ratio efficiency of the mean square in the general Gauss-Markov model, The Fourth China-Japan Symposium on Statistics, 17–19.

    Google Scholar 

  • GAO, D. D., WANG, G. L. (1990), The efficiency of generalized least squares, System Sciences and Mathematical science, 10: 125–130.

    Google Scholar 

  • HABERMAN, S. J. (1975), How much do Gauss-Markov and the least square estimates differ? A coordinate free approach, Ann. Statist., 3: 982–990.

    Article  Google Scholar 

  • KNOFF, M. (1975), On the minimum efficiency of the least squares, Biometrika, 62: 129–132.

    Article  Google Scholar 

  • RAO, C. R. (1975), The inefficiency of least squares: extensions of the Kantorovich inequality, Linear Algebra and its Applications, 70: 249–255.

    Google Scholar 

  • WANG, S. G. (1982), The euclidian norm bound of difference between LSE and BLUE of mean vector in linear model, Acta Math. Appl. Sinica, 5: 190–192.

    Google Scholar 

  • WANG, S. G., YAN, H. (1989), Kantorovich type inequality and measures of inefficiency of the GLSE, Acta Math. Appl. Sinica, 5: 372–384.

    Article  Google Scholar 

  • WANG, X. R., ZHANG, J. L., Chen, J. B. (1994), All admissible linear estimators of regression coefficients and parameters in variance components models, Acta Math. Sinica, 5: 653–662.

    Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Egle, K., Zhan, J. (1999). Efficiencies of Least Squares in Linear Models. In: Gaul, W., Schader, M. (eds) Mathematische Methoden der Wirtschaftswissenschaften. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12433-8_11

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  • DOI: https://doi.org/10.1007/978-3-662-12433-8_11

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-12434-5

  • Online ISBN: 978-3-662-12433-8

  • eBook Packages: Springer Book Archive

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