Showing papers by "Herman Chernoff published in 1977"

A subset selection problem employing a new criterion

Abstract: Publisher Summary The extensive literature on ranking and selection procedures depends heavily on the use of two alternative criteria that are philosophically out of tune with the decision theoretic framework. This chapter describes a new criterion for selecting a subset of k populations and also describes two subset selection procedures introduced by Gupta, Desu, and Sobel in terms of this criterion. Results based on a Monte Carlo studies show that the Gupta procedure is highly efficient. The criterion used in the chapter is advanced in terms of a natural loss function for only one potential application and is not intended to be universally relevant. Calculations are carried out in an invariant Bayesian framework using normal distributions and normal priors. Comparisons are based on Monte Carlo simulations for the case of k = 8 populations.

A satellite control problem

Abstract: : A numerical approach is described for calculating the optimal policy in the stochastic control problem of keeping a satellite close to a fixed point in space when it is subject to random forces The random forces are modelled by Brownian Motion A policy is evaluated in terms of its long run expected average cost The running costs consist of a charge for fuel used plus a charge of x sub 1 squared per unit of time when the satellite is x sub 1 units away from the target The space is one-dimensional The method used is to apply backward induction to a bounded discrete space, discrete time version of the problem Incidentally a solution is presented for the deterministic version of the problem where there are no random forces