Estimation of parameters in a linear model

Rao, C. Radhakrishna (1976) Estimation of parameters in a linear model Annals of Statistics, 4 (6). pp. 1023-1037. ISSN 0090-5364

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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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