Tests for independence in non-parametric heteroscedastic regression models

Abstract

Consistent procedures are constructed for testing independence between the regressor and the error in non-parametric regression models. The tests are based on the Fourier formulation of independence, and utilize the joint and the marginal empirical characteristic functions of the regressor and of estimated residuals.

The asymptotic null distribution as well as the behavior of the test statistic under alternatives is investigated. A simulation study compares bootstrap versions of the proposed tests to corresponding procedures utilizing the empirical distribution function.

Keywords

• Test of independence
• empirical characteristic function
• kernel regression estimator
• bootstrap