Abstract
We consider an approach yielding a minimax estimator in the linear regression model with a priori information on the parameter vector, e.g., ellipsoidal restrictions. This estimator is computed directly from the loss function and can be motivated by the general Pitman nearness criterion. It turns out that this approach coincides with the projection estimator which is obtained by projecting an initial arbitrary estimate on the subset defined by the restrictions.
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References
Fountain R. L.: 1991, Pitman closeness comparison of linear estimators: A canonical form,Comm. Statist. Theory Methods 20(11), 3535–3550.
Peddada S. D. and Khattree R.: 1986, OnPitman nearness and variance of estimators,Comm. Statist. Theory Methods 15(10), 3005–3017.
Pilz J.: 1991,Bayesian Estimation and Experimental Design in Linear Regression Models, 2nd edn, Wiley, New York.
Pitman E. J. G.: 1937, The closest estimates of statistical parameters,Proc. Cambridge Philosoph. Soc. 33, 212–222.
Rothenberg T. J.: 1973,Efficient Estimation with A Priori Information, Yale University Press, New Haven.
Schmidt K. and Stahlecker P.: 1995, Reducing maximum risk of regression estimators by polyhedral projection,J. Statist. Comput. 52, 1–15.
Stahlecker P.: 1987,A priori Information und Minimax-Schätzung im linearen Regressionsmodell, Mathematical Systems in Economics 108, Verlag Athenäum, Frankfurt-am-Main.
Stahlecker P. and Trenkler G.: 1993, Minimax estimation in linear regression with singular covariance structure and polyhedral constraints,J. Statist. Plann. Inference 36, 185–196.
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Stahlecker, P., Knautz, H. & Trenkler, G. Minimax adjustment technique in a parameter restricted linear model. Acta Appl Math 43, 139–144 (1996). https://doi.org/10.1007/BF00046994
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DOI: https://doi.org/10.1007/BF00046994