Beatlestrap

Abstract

The bootstrap of test statistics requires the re-estimation of the model's parameters for each bootstrap sample. When parameter estimates are not available in closed form, this procedure becomes computationally demanding as each replication requires the numerical optimization of an objective function. This paper investigates the feasibility of the Beatlestrap, an optimization-free approach to bootstrap. It is shown that, ex-post, M-estimators may be expressed in terms of simple arithmetic averages therefore reducing the bootstrap of Wald statistics to the bootstrap of averages. Similarly, it is shown how the Lagrange Multiplier and the Likelihood Ratio statistics may be bootstrapped bypassing the objective function's multiple optimizations. The proposed approach is extended to simulation based Indirect Estimators. The finite sample properties of Beatlestrap are investigated via Monte Carlo simulations.