Testing the equality of nonparametric regression curves based on Fourier coefficients

Abstract

In this work we propose a new methodology for the comparison of two regression functions $f_1$ and $f_2$ in the case of homoscedastic error structure and a fixed design. Our approach is based on the empirical Fourier coefficients of the regression functions $f_1$ and $f_2$ respectively. As our main results we obtain the asymptotic distribution of the test statistic under the null hypothesis $f_1 = f_2$ and local and global alternatives. A simulation study is conducted to investigate the finite sample performance of our test.