| Gaussian processes are not uncommon in various fields of science such as engineering, genomics, quantitative finance and astronomy, to name a few. In fact, such processes are special cases in a broader class of data known as functional data. When the underlying mean response of a process is a function, the resulting data from these processes are functional responses and specialized statistical tools are required in their analysis. The methodology discussed in this work offers non-parametric tests that can detect differences in such data with greater power and good control of Type-I error over existing methods. The incorporation of Wavelet Transforms makes the test an efficient approach due to its de-correlation properties. These tests are designed primarily to handle functional responses from multiple treatments simultaneously and generally are extensible to high dimensional data. The sparseness introduced by Wavelet Transforms is another advantage of this test when compared to traditional tests. In addition to offering a theoretical framework, several applications of such tests in the fields of engineering, genomics and quantitative finance are also discussed. |
