22 research outputs found
On the optimal choice of the number of empirical Fourier coefficients for comparison of regression curves
The paper is devoted to the elaboration of an efficient approach for comparison
of two regression curves based on the empirical Fourier coefficients of regression
functions. For the problem of testing for the equality of the two unknown functions
in the case of homoscedastic error structure and observation at equidistant points, we
derive a new procedure with adaptive choice of the number of the coefficients used in
the hypotheses testing. Our approach is based on approximation of the most powerful
test using the full knowledge of the regression functions. The results are justified by
theoretical arguments and the superiority of the new procedure is also confirmed by a
simulation study