Estimation-robust model checking for generalized partially linear models

R. Gaio, R. Costa-Miranda, W. González-Manteiga

Recent developments have established an estimation-robust testing of conditional moment restrictions (CMR) in parametric models, using Neyman-orthogonal Gaussian processes and a fast bootstrap. We extend it to generalized partially linear models, where the nonparametric component leads to an infinite-dimensional nuisance parameter space.
Based on a local polynomial iteratively reweighted least squares procedure, we reformulate the CMR in a finite-dimensional parameter space, with the dimension growing at the sample size rate.
We establish that using zero mean and distance kernels is equivalent to a specific integrated conditional moment testing. By handling the slow convergence rate of the nonparametric estimators, we prove the convergence of the empirical test statistic under the null hypothesis.
A simulation study shows the test is well calibrated for the type-I error rate. Despite a loss in power, it gains in computational efficiency against the full-bootstrap counterpart.

Keywords: generalized partially linear models, model checking, local polynomial estimation, Neyman-orthogonal kernels

SI: Portuguese Statistical Society invited session in Statistics and Probability
September 2, 2026  11:20 AM
Aula 29

N. M. Brites, J. Brazão, M. Reis

L. F. Meira Machado

C. Tenreiro