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Nonparametric selection of regressors: the nonnested case. (English) Zbl 0860.62039
We propose a consistent and directional testing procedure for discriminating between two sets of regressors without specifying either the functional form of the regressions or the distribution of the residuals. Our test statistic uses the empirical mean square error (MSE) from a nonparametric (kernel) regression. In Section 2, the empirical MSE is shown to estimate consistently the residual variance, whether the regression errors are homoscedastic or not. Moreover, it is asymptotically normally distributed with a parametric rate of convergence and is asymptotically efficient in the semiparametric sense. Building on this result, Section 3 presents our testing procedure. We discuss a crucial condition for its validity which relates to the definition of “generalized nonnested regressions”. Some simulation results using automatically chosen bandwidths are presented in Section 4. They suggest that the test has good power and size properties even in samples of small size. The Appendix collects our proofs.

MSC:
62G10 Nonparametric hypothesis testing
62G07 Density estimation
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