We develop a novel approach to build checks of parametric regression models when many regressors are present, based on a class of sufficiently rich semiparametric alternatives, namely single-index models. We propose an omnibus test based on the kernel method that performs against a sequence of...

To study the influence of a bandwidth parameter in inference with conditional moments, we propose a new class of estimators and establish an asymptotic representation of our estimator as a process indexed by a bandwidth, which can vary within a wide range including bandwidths independent of the...

A procedure for testing equality across nonparametric regressions is proposed. The procedure allows for any dimension of the explanatory variables and for any number of subsamples. We consider the case of random explanatory variables and allow the designs of the regressors and the number of...

A procedure for testing the signicance of a subset of explanatory variables in a nonparametric regression is proposed. Our test statistic uses the kernel method. Under the null hypothesis of no effect of the variables under test, we show that our test statistic has a nhp2/2 standard normal...

I propose a new theoretical framework to assess the approximate validity of overidentifying moment restrictions. Their approximate validity is evaluated by the divergence between the true probability measure and the closest measure that imposes the moment restrictions of interest. The divergence...

In empirical research, one commonly aims to obtain evidence in favor of restrictions on parameters, appearing as an economic hypothesis, a consequence of economic theory, or an econometric modeling assumption. I propose a new theoretical framework based on the Kullback–Leibler information to...

A procedure for testing the signicance of a subset of explanatory variables in a nonparametric regression is proposed. Our test statistic uses the kernel method. Under the null hypothesis of no effect of the variables under test, we show that our test statistic has a nhp2/2 standard normal...