Tests for Symmetric Error Distribution in Linear and Nonparametric Regression Models

Abstract

In linear and nonparametric regression models, the problem of testing for symmetry of the distribution of errors is considered. We propose a test statistic which utilizes the empirical characteristic function of the corresponding residuals. The asymptotic null distribution of the test statistic as well as its behavior under alternatives is investigated. A simulation study compares bootstrap versions of the proposed test to other more standard procedures.

Keywords:

• Empirical characteristic function
• Goodness-of-fit test
• Kernel regression estimator
• Symmetry test
• Wild bootstrap

Mathematics Subject Classification:

• 62G8
• 62G10
• 62G20

Acknowledgments

The work of M. Hu\v sková has been supported by grant GAČR 201/09/0775. The work of Simos Meintanis has been supported by grant number KA 70/4/7658 of the program ‘Kapodistrias’ of the special account for research of the National and Kapodistrian University of Athens.