Optimum Design of Serial Measurement Trees

Suppose some or all of p predictor variables X 1 , X 2 ; : : :; X p may be measured and their values used to predict a response Y. When measurement costs are considered, it may be advantageous to measure predictors serially, deciding adaptively which variable to measure next with an option to stop taking measurements and predict Y at any point during the measurement process. In this article we derive optimal prediction strategies of a serial type under a cost structure that combines measurement costs with the usual prediction{error loss function. It is assumed that the joint distribution of Y , X 1 , X 2 ; : : :; X p is known. The results provide a theoretical basis upon which estimation of optimum serial measurement plans may be addressed.