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Numerical Classification of Biased Estimators

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Conceptual and Numerical Analysis of Data

Abstract

In recent years some alternatives to the least squares estimation function in the linear model have been introduced. Most of these functions can be represented as a linear or non-linear transformation of the least squares function. It is shown that these estimation functions can be derived as minimum norm estimation functions in the class of linear transforms of the least squares estimation function. In addition a numerical classification of these functions is given which yields an appropriate algorithm for computation.

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References

  • BAUR, F. (1984). Einige lineare und nicht-lineare Alternativen zum Kleinst-Quadrate-Schätzer im verallgemeinerten linearen Modell, Anton Hain, Königstein/Ts.

    MATH  Google Scholar 

  • GOLUB, G./REINSCH, C. (1970). Singular value decomposition and least squares solutions, Numer. Math., 14, 403–420.

    Article  MathSciNet  MATH  Google Scholar 

  • HOERL, A.E./KENNARD, R.W. (1970). Ridge regression: Biased estimation for nonorthogonal problems, Technometrics, 12, 55–67.

    Article  MATH  Google Scholar 

  • JUDGE, G.G. (1984). Pre-Test and Stein-Rule estimators, Some new results, Journal of Econometrics, 25, North Holland, Amsterdam.

    MATH  Google Scholar 

  • MAYER, L.S./WILLKE, T.A. (1973). On Biased Estimation in Linear Models, Technometrics, 15, 497–508.

    Google Scholar 

  • MüLLER, P. (1984). Entscheidungstheoretisch begründete Schätzverfahren, Anton Hain, Königstein/Ts.

    MATH  Google Scholar 

  • STEIN, C. (1956). Inadmissibility of the usual estimator for the normal mean of a multivariate normal distribution, Proc. of the 3rd Berkely Symp. on Mathematical Statistics and Probability, 1, 197–206.

    Google Scholar 

  • TRENKLER, G. (1978). An iteration estimator for the linear model, Physika Verlag, Würzburg.

    Google Scholar 

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© 1989 Springer-Verlag Berlin · Heidelberg

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Müller, P. (1989). Numerical Classification of Biased Estimators. In: Optiz, O. (eds) Conceptual and Numerical Analysis of Data. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75040-3_12

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  • DOI: https://doi.org/10.1007/978-3-642-75040-3_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51641-5

  • Online ISBN: 978-3-642-75040-3

  • eBook Packages: Springer Book Archive

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