Introduction

This chapter proposes a testing procedure for discriminating between alternative sets of regressors in a non-parametric context. The literature on non-parametric testing of regression models is quite extensive. Non-parametric methods have been used for specification testing of a parametric model against a non-parametric alternative, see Eubank and Spiegelman (1990), Hall and Hart (1990), Hong and White (1991), Wooldridge (1992), Härdle and Mammen (1993), Whang and Andrews (1993), Horowitz and Härdle (1994), de Jong and Bierens (1994), Fan and Li (1996) and Delgado and Stengos (1994), to mention only a few.

Discriminating between non-nested sets of regressors is a well motivated problem. Existing tests assume a particular functional form of the regression function and are consistent in the direction of precisely parameterized alternatives, see Cox (1961, 1962), Pesaran (1974), Davidson and MacKinnon (1981) and Fisher and McAleer (1981), also see MacKinnon (1992) for a survey. Recently Delgado and Stengos (1994) have proposed an extension of the J-test of Davidson and MacKinnon that is consistent against non-parametric alternatives. The above test still assumes a particular parametric regression curve under the null hypothesis. Hence, it is still not robust to functional misspecification. In this chapter, we propose to test a non-parametric regression model in the direction of a non-parametric non-nested alternative.