Confidence intervals based on estimators with unknown rates of convergence

Confidence interval construction for an unknown parameter typically requires precise knowledge of the convergence rate of a point estimator targeting the parameter and explicit specification of the asymptotic distribution of the (standardized) point estimator. A subsampling method is presented here for obtaining confidence intervals which requires very little knowledge of the estimator's asymptotic distribution or of its convergence rate; the asymptotic distribution may be non-Normal, and the convergence rate may differ from the familiar n(1/2). Serial dependence is allowed in the observed data sequence, and the dependence mechanism can be unknown. Under mild conditions, the intervals asymptotically obtain the nominal coverage level and interval width shrinks to zero as sample size increases. Finite-sample behavior of the proposed confidence interval is studied by example, simulation, and Edgeworth expansion. (C) 2003 Elsevier B.V. All rights reserved.