Stochastic Estimation and Testing

Abstract

Stochastic procedures are randomized tests, estimates and confidence sets with two properties: (i) They are functions of an original sample and one or more artificially constructed auxiliary samples. (ii) They become nearly nonrandomized when the auxiliary samples increase in size. The stochastic procedures of this paper, which arise as approximations to numerically intractable procedures, involve iterated bootstrap techniques and random sampling schemes over abstract populations. A general methodology is applied to the asymptotic study of stochastic minimum distance tests, stochastic maximum likelihood estimates, stochastic confidence bands and several other stochastic procedures.