مرکز منطقه ای اطلاع رساني علوم و فناوري - Estimating a binomial parameter with finite memory

Abstract :

This article treats the asymptotic theory of estimating a binomial parameter $p$ with time-invariant finite memory. The approach taken to this problem is as follows. A decision rule is a pair $(t,a)$ in which $t$ fixes the transition function of a finite automaton, and $a$ is a vector of estimates of $p$ . Attention is restricted to automata whose transition functions allow transitions only between adjacent states. Rules $(t,a)$ for which $t$ satisfies this restriction are termed tridiagonal. For the class of prior distributions on [0,1] which have continuous density functions, we study the performance of a corresponding class of tridiagonal rules ${ (t^{\\ast },a^{\\ast }) }$ relative to quadratic loss functions. These rules display sensitivity to the shape of the prior, and have the advantage that the Bayes estimate $a^{\\ast }$ (given $t^{\\ast }$ ) is easily computed. Within the class of all tridiagonal rules, a particular rule $(t^{\\ast },a^{\\ast })$ is shown, for memory size up to 30, to be locally admissible and minimax as well as locally Bayes with respect to the uniform prior.

Keywords :

Decision procedures; Finite-memory methods; Parameter estimation; Automata; Computer displays; Estimation theory; Minimax techniques; Parameter estimation; Performance loss; Random variables; Shape; Stochastic processes; Testing;