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November, 1976 Estimation of Parameters in a Linear Model
C. Radhakrishna Rao
Ann. Statist. 4(6): 1023-1037 (November, 1976). DOI: 10.1214/aos/1176343639


The first lecture in this series is devoted to a survey of contributions during the last five years to estimation of parameters by linear functions of observations in the Gauss-Markoff model. Some new results are also given. The classes of BLE (Bayes linear estimators) and ALE (admissible linear estimators) are characterized when the loss function is quadratic. It is shown that ALE's are either BLE's or limits of BLE's. Biased estimators like ridge and shrunken estimators are shown to be special cases of BLE's. Minimum variance unbiased estimation of parameters in a linear model is discussed with the help of a projection operator under very general conditions.


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C. Radhakrishna Rao. "Estimation of Parameters in a Linear Model." Ann. Statist. 4 (6) 1023 - 1037, November, 1976.


Published: November, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0336.62055
MathSciNet: MR420979
Digital Object Identifier: 10.1214/aos/1176343639

Primary: 62C10
Secondary: 62C15 , 62J05

Keywords: admissible estimator , Bayes estimator , best homogeneous linear estimator , Gauss-Markoff model , Minimax estimator , ridge estimator

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 6 • November, 1976
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