Contrast tests for groups of functional data

Abstract

Functional analysis of variance (ANOVA) models are often used to compare groups of functional data. Similar to the traditional ANOVA model, a common follow-up procedure to the rejection of the functional ANOVA null hypothesis is to perform functional linear contrast tests to identify which groups have different mean functions. Most existing functional contrast tests assume independent functional observations within each group. In this article, we introduce a new functional linear contrast test procedure that accounts for possible time dependency among functional group members. The test statistic and its normalized version, based on the Karhunen–Loève decomposition of the covariance function and a weak convergence result of the error processes, follow respectively a mixture chi-squared and a chi-squared distribution. An extensive simulation study is conducted to compare the empirical performance of the existing and new contrast tests. We also present two applications of these contrast tests to a weather study and a battery-life study. We provide software implementation and example data in the Supplementary Material.