Asymptotic refinements of nonparametric bootstrap for quasi‐likelihood ratio tests for classes of extremum estimators

Abstract

We study the asymptotic refinements of nonparametric bootstrap for quasi‐likelihood ratio type tests of nonlinear restrictions. The bootstrap method applies to extremum estimators, such as quasi‐maximum likelihood and generalized method of moments estimators, among others. Unlike existing parametric bootstrap procedures for quasi‐likelihood ratio type tests, this bootstrap approach does not require any specific parametric assumption on the data distribution, and constructs the bootstrap samples in a fully nonparametric way. We derive the higher‐order improvements of the nonparametric bootstrap compared to procedures based on standard first‐order asymptotic theory. We show that the magnitude of these improvements is the same as those of parametric bootstrap procedures currently proposed in the literature. Monte Carlo simulations confirm the reliability and accuracy of the nonparametric bootstrap.