Testing symmetry in nonparametric regression models

Testing symmetry in nonparametric regression models

In a recent paper Ahmad and Li (1996) proposed a new test for symmetry of the error distribution in linear regression models and proved asymptotic normality for the distribution of the corresponding test statistic under the null hypothesis and consistency under xed alternatives. The present paper has three purposes. On the one hand we derive the asymptotic distribution of the statistic consider...

Testing symmetry in nonparametri regression models

Nonparametric Least Squares Regression and Testing in E Conomic Models

This paper proposes a tractable and consistent estimator of the (possibly multi-equation) nonparametric regression model. The estimator is based on least squares over sets of functions bounded in Sobolev norm and is closely related to penalized least squares. We establish consistency and rate of convergence results as well as asymptotic normality of the (suitably standardized) sum of squared re...

Minimax rates for nonparametric speci cation testing in regression models

In the context of testing the speci cation of a nonlinear parametric regression function, we study the power of speci cation tests using the minimax approach. We determine the maximum rate at which a set of smooth local alternatives can approach the parametric model while ensuring consistency of a test uniformly against any alternative in this set. We show that a smooth nonparametric testing pr...

Testing for Symmetric Error Distribution in Nonparametric Regression Models

For the problem of testing symmetry of the error distribution in a nonparametric regression model, we investigate the asymptotic properties of the difference between the two empirical distribution functions of estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussian process is shown. The covariance structure of this process dep...