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On Limits of Uniquely Best Linear Estimators

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Abstract

In a general linear model, it is shown that all admissible linear estimators are limits of linear estimators that are uniquely best at some point in an extended parameter set. The principal result shows that a linear estimator that is uniquely best at a pointW 2 among multiple linear estimators that are best at a pointW 1 is the limit of uniquely best estimators at points approachingW 1 along the line joiningW 1 andW 2.

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Authors and Affiliations

  1. Department of Experimental Statistics, College of Agriculture, Louisiana State University, 70803-5606, Baton Rouge, LA, USA

    Lynn Roy LaMotte

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  1. Lynn Roy LaMotte
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Additional information

Research supported in part by U.S.A.F. Aerospace Research Laboratories under contract F33615-71-C-1463, summer 1973, and in part by Grant DMS-9104811 from the National Science Foundation.

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LaMotte, L.R. On Limits of Uniquely Best Linear Estimators. Metrika 45, 197–211 (1997). https://doi.org/10.1007/BF02717103

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  • DOI: https://doi.org/10.1007/BF02717103

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