ruth@utstat.uucp (Ruth Croxford) (02/07/89)
Topic: How should one choose the loss function to estimate the covariance
structure of a generalized linear model?
Speaker: Martin Bilodeau, Dept of Statistics, University of Toronto
Date: 4:00 p.m., Thursday, February 9, 1989
Place: room 2110, Sidney Smith Hall, 100 St George St., University of Toronto
Abstract:
In a generalized linear model, under certain conditions, the covariance matrices
of a two-stage Aitken estimator and the Gauss-Markov estimator are related via
Kariya's inequality of the form
Cov(beta hat(omega)) <= Cov(beta hat(omega hat)) <=
psi sub gamma [L(gamma, gamma hat)] Cov(beta hat(omega)),
where the true covariance matrix omega of the response is a function of an
estimable parameter gamma. This inequality is used as a basis for defining
a loss function to estimate gamma. Two models ae analyzed: the seemingly
unrelated regressions and the heteroscedastic model. In both cases, the
loss function is univariant with respect to an appropriate group of
transformations and the minimum risk equivariant estimators obtained.
This approach reduces the degree of arbitrariness for choosing a loss function.
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