Wavelet Functional ANOVA, Bayesian False Discovery Rate, and Longitudinal Measurements of Oxygen Pressure in Rats

Abstract

Linear models can be functional in terms of independent or response variables or both. In functional ANOVA-type models often used to model longitudinal measurements and general time series, however, all components have a functional form. One of the main problems in inference using such models is the intrinsic dependence in “time” that makes pointwise inference difficult. We propose performing the inference in the wavelet domain instead of the time domain. Transformations by orthogonal wavelets preserve the structure of the linear model and, at the same time, decorrelate the data. The proposed methodology is applied to longitudinal measurements from experiments measuring oxygen pressure in tumor-bearing rats.