Dimension-reduction type test for linearity of a stochastic regression model

Abstract

This article investigates the test for linearity of a multivariate stochastic regression model. The use of nonparametric regression procedures for developing regression diagnostics has been the subject of several recent research efforts. However, when the dimension of the regressor is large, some traditional nonparametric methods, such as kernel estimation, may be inefficient. We in this article suggest two test statistics based on projection pursuit technique and kernel method. The tests proposed are consistent against all fixed smooth alternatives to linearity and are asymptotically distribution-free for the distribution of the error. Furthermore, the tests are applied to an example of real-life data and some simulated data sets to demonstrate the availability of the tests proposed.