Locally Robust Kernel Specification Tests for Conditional Moment Restrictions

2026-07-27

AI Summary

This study addresses the challenge of specification testing in conditional moment models under high-dimensional nuisance parameters, where conventional approaches relying on asymptotically linear estimators struggle to accommodate modern machine learning methods. The authors propose a kernel-based locally robust testing framework that uniquely integrates Neyman-orthogonal moments, cross-fitting, and reproducing kernel Hilbert space techniques to achieve first-order insensitivity to estimation errors in nuisance parameters. Under mild convergence rates for nuisance estimators, the method ensures oracle equivalence between feasible and infeasible tests and precisely characterizes local power. Employing a fast multiplier bootstrap, the framework demonstrates excellent finite-sample performance across diverse applications—including specification tests for high-dimensional linear and logistic regression, significance testing in machine learning regression, and tests for constant conditional treatment effects—as validated by Monte Carlo simulations and empirical analysis.

Abstract

We develop kernel-based specification tests for semiparametric conditional moment models with high-dimensional nuisance parameters, extending existing conditional moment tests---which typically require asymptotically linear nuisance estimators---to accommodate modern machine-learning methods. The proposed locally robust kernel tests combine Neyman-orthogonal moments, cross-fitting, and reproducing kernel Hilbert space methods, yielding inference that is first-order insensitive to nuisance estimation error. We establish oracle equivalence between the feasible and infeasible test processes under local alternatives and weak nuisance-rate conditions, and characterize the resulting local power. A fast multiplier bootstrap avoids nuisance re-estimation. Applications include specification testing in high-dimensional linear and logistic regression, significance testing with machine-learning regressions, and tests of constant conditional treatment effects. Monte Carlo simulations and an application to the National Supported Work program illustrate the finite-sample performance of the proposed tests.

Problem

• conditional moment restrictions
• specification testing
• nuisance parameters
• machine learning
• high-dimensional models

Innovation

• locally robust
• kernel specification test
• Neyman-orthogonal moments
• cross-fitting
• reproducing kernel Hilbert space