Tests for equality of curves via wavelets

Abstract

In this article, we develop tests for equality of response curves. We assume that the mathematical expression of the response curves are unknown. Consequently, we exploit the adaptive properties of wavelets to construct a wavelet representation of the curves. Then, we develop an approach which combines the False Discovery Rate (FDR) technique and the universal thresholding approach, widely used in data denoising, for detecting differences between the curves. We also discuss some methods based on the general F-test. We consider several examples under a variety of conditions such as unequal variances, unequal number of observations, and distinct design points. The size and power performances of the tests are reported. We present two real examples at the end of this article.