Asymptotic Refinements of a Fully Nonparametric Bootstrap for Quasi-Likelihood Ratio Tests of Extremum Estimators

We study the asymptotic refinements of a fully nonparametric bootstrap approach for quasi-likelihood ratio type tests of nonlinear restrictions. This bootstrap method applies to extremum estimators, such as quasi-maximum likelihood and generalized method of moments estimators. Unlike existing parametric bootstrap procedures for quasi-likelihood ratio type tests, this boot-strap 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. In particular, we show that the magnitude of these improvements is the same as those of the parametric bootstrap procedures currently proposed in the literature. Monte Carlo simulations confirm the reliability and accuracy of the nonparametric bootstrap approach.