A geometrical setting is constructed, based on Hilbert space, in which the asymptotic properties of estimators can be studied. Estimators are defined in the context of parametrised models, which are treated as submanifolds of an underlying Hilbert manifold, on which a parameter-defining mapping...

When a model is nonlinear, boostrap testing can be expensive because of the need to perform at least one nonlinear estimation for every bootstrap sample. We show that it may be possible to reduce computational costs by performing only a fixed, small number of Newton steps or artificial...

We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic...

In this paper we are interested in inference based on heteroskedasticity consistent covariance matrix estimators, for which the appropriate bootstrap is a version of the wild bootstrap. Simulation results, obtained by a new very efficient methos, show that all wild bootstraps tests exhibit...

Bootstrap tests are tests for which the significance level is calculated by some sort of bootstrap procedure, which may be parametric or nonparametric. We provide a theoretical framework in which to study the size distorsions of bootstrap P values. We show that, in many circumstances, the size...

Most confidence intervals, whether based on asymptotic theory or the bootstrap, are implicitly based on inverting a Wald test. Since Wald test statistics are not invariant under nonlinear reparametrizations of the restrictions they test, confidence intervals based on them are not invariant...