Second order accurate inference for nonparametric estimating equations models

This paper considers pointwise inference for nonparametric estimating equations models.The paper proposes two general test statistics that are based on a local version of the Generalized Empirical Likelihood (GEL) approach that can be used to test simple hypotheses about the unknown infinite dimensional parameters and to test for the correct specification of the chosen nonparametric estimating equations model.The paper shows that among the class of the proposed GEL test statistics, the empirical likelihood ratio is the only one admitting a Bartlett correction, however by appropriately modifying the other GEL based test statistics, it is still possible to obtain second order accurate inferences.The paper also proposes a new (local) version of the so-called efficient bootstrap that delivers the same level of second order accuracy as that of the (modified) GEL test statistics for the correct specification of the chosen nonparametric estimating equations model.Finally, the paper uses simulations and a real data example to illustrate the finite sample properties and applicability of the proposed inference methods.