An Optimal Drawing Policy for a Random Urn Scheme

Abstract

Consider a causal stationary AR(p) process with Gaussian white noise. We construct asymptotic confidence regions for unknown parameters by obtaining very weak expansions for the distributions of an approximate pivotal quantity. First the likelihood is converted into a form close to a standard multivariate normal density. Then a version of Stein's Identity is applied to obtain an expression of posterior expectations, from which an asymptotic expansion is readily guessed. We apply the results to find confidence intervals for the parameters and compare with simulation experiments for an AR(2) model.