| Abstract: | Suppose that data (y, z) are observed from two regression models, y = f(x) + [epsilon] and z = g(x) + [eta]. Of interest is testing the hypothesis H : f [triple bar] g without assuming that f or g is in a parametric family. A test based on the difference between linear, but nonparametric, estimates of f and g is proposed. The exact distribution of the test statistic is obtained on the assumption that the errors in the two regression models are normally distributed. Asymptotic distribution theory is outlined under more general conditions on the errors. It is shown by simulation that the test based on the assumption of normal errors is reasonably robust to departures from normality. A data analysis illustrates that, in addition to being attractive descriptive devices, nonparametric smoothers can be valuable inference tools. |
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