We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

This paper introduces and analyzes a procedure called Testing-Based Forward Model Selection (TBFMS) in linear regression problems. This procedure inductively selects covariates that add predictive power into a working statistical model before estimating a final regression. The criterion for...

For the problem of testing symmetry of the error distribution in a nonparametric regression model we propose as a test statistic the difference between the two empirical distribution functions of estimated residuals and their counterparts with opposite signs. The weak convergence of the...

In this paper we describe some general methods for constructing goodness of fit tests in nonparametric regression models. Our main concern is the development of statisticial methodology for the assessment (validation) of specific parametric models M as they arise in various fields of...