Abstract
In the present paper estimators of the signal-to-noise are given. A simulation study is conducted in order to see how the proposed estimators perform relative to the naive estimator by way of scalar risk comparison. The results favour our suggested estimators.
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Brook, R.J. andMoore, T. (1980): On the expected length of the least squares coefficient vector.Journal of Econometrics 12, 245–246.
Box, G.E.P. andMuller, M.E. (1958): A note on the generation of normal deviates.Annals of Mathematical Statistics 28, 610–611.
Farebrother, R.W. (1976): Further results on the mean square error of ridge regression.Journal of the Royal Statistical Society B38, 248–250.
Gibbons, D. G. (1981): Simulation study of some ridge estimators.Journal of the American Statistical Association 76, 131–139.
Gnot, S., Trenkler, G. andZymslony, R.J. (1995): Non-negative minimum biased quadratic estimation in the linear regression model.Journal of Multivariate Analysis 54, 113–125.
Hoerl, A.E. andKennard, R.W. (1970a): Ridge regression: Biased estimation for non-orthogonal problems.Technometrics 12, 55–67.
Hoerl, A.E. andKennard, R.W. (1970b): Ridge regression: Applications to non-orthogonal problems.Technometrics 12, 69–82.
Liski, E.P. (1982): A test of the mean square error criterion for shrinkage estimators.Communications in Statistics B11, 543–562.
Marquardt, D.W. (1970): Generalised inverses, ridge regression, biased linear estimation and non-linear estimationTechnometrics 12, 591–612.
Marquardt, D.W. andSnee, R.D. (1975): Ridge regression in practice.American Statistician 29, 497–508.
McDonald, G.C. andGalarneau, D.I. (1975): A Monte Carlo evaluation of some ridge-type estimators.Journal of the American Statistical Association 70, 407–416.
Mayer, L.S. andWillke, T.A. (1973): On biased estimation in linear models.Technometrics 15, 497–508.
Mood, A.M., Graybill, F.A. andBoes, D.C. (1982):Introduction to the theory of statistics, 3rd Edition. McGraw-Hill, Auckland.
Price, J.M. (1982): Comparison among regression estimators under the generalised mean square error criterion.Communications in Statistics A11, 1965–1984.
Schmidt, B. (1998):Signals-to-Noise Schätzungen im linearen Regression-smodell. Masters Thesis, University of Dortmund.
Subrahmanya, M.T. (1970): A note on non-negative estimators of positive parameters.Metrika 16, 19–23.
Theobald, C.M. (1974): Generalisations of mean square error applied to ridge regression.Journal of the Royal Statistical Society B36, 103–106.
Trenkler, D. (1986):Verallgemeinerte Ridge-Regression. In: Mathematical Systems in Economics 104. Anton Hain Verlag. Frankfurt/Main.
Trenkler, G. (1981):Biased Estimators in the Linear Regression Model. In: Mathematical Systems in Economics 58. Oelgeschlager, Gunn und Hain, Massachussets.
Wencheko, E. (1993):Die Schätzung des Signals und verwandter Parameterfunktionen. Doctoral Thesis, University of Dortmund.
Wichern, D.W. andChurchill, G.A. (1978): A comparison of ridge estimators.Technometries 20, 301–311
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Wencheko, E. Estimation of the signal-to-noise in the linear regression model. Statistical Papers 41, 327–343 (2000). https://doi.org/10.1007/BF02925926
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DOI: https://doi.org/10.1007/BF02925926