A frequentistic and bayesian analysis of zellner's economic regression model under an informative prior

Abstract

Vector-valued observations Y₁,Y₂,... arrive sequentially and satisfy the general linear model The X_i's are either random or known matrices and, given β and σ², the are iid The parameter β is estimated by the Bayes estimator under the conjugate prior and subject to a loss structure that is the sum of the cost due to sampling and a predictive loss due to estimation error. We show that the myopic rule is asymptotically nondeficient in that the difference between its Bayes risk and the Bayes risk of the optimal procedure is of smaller order of magnitude than c, the cost of a single observation, as c → 0. The myopic stopping rule is also examined frequentistically through the use of nonlinear renewal theory.

Keywords:

• General 1inear model
• nonlinear renewal theory
• sequential estimation
• large sample theory
• first passage stopping time
• myopic stopping rule
• Bayes risk