Testing the equality of two regression curves using linear smoothers

Suppose that data (y, z) are observed from two regression models, y = f(x) + [var epsilon] and z = g(x) + [eta]. Of interest is testing the hypothesis H: f [triple bond; length as m-dash] 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.