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.
Publié le : 1976-11-14
Classification:
Gauss-Markoff model,
ridge estimator,
admissible estimator,
minimax estimator,
Bayes estimator,
best homogeneous linear estimator,
62C10,
62C15,
62J05
@article{1176343639,
author = {Rao, C. Radhakrishna},
title = {Estimation of Parameters in a Linear Model},
journal = {Ann. Statist.},
volume = {4},
number = {1},
year = {1976},
pages = { 1023-1037},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343639}
}
Rao, C. Radhakrishna. Estimation of Parameters in a Linear Model. Ann. Statist., Tome 4 (1976) no. 1, pp. 1023-1037. http://gdmltest.u-ga.fr/item/1176343639/