Wavelet analysis of variance box plot

Functional box plots satisfy two needs; visualization of functional data, and the calculation of important box plot statistics. Data visualization illuminates key characteristics of functional sets missed by statistical tests and summary statistics. The calculation of box plot statistics for functional sets permits a novel comparison more suited to functional data. The functional box plot uses a depth method to visualize and rank smooth functional curves in terms of a mean, box, whiskers, and outliers. The functional box plot improves upon other classic functional data analysis tools such as functional principal components and discriminant analysis for outlier detection. This research adds wavelet analysis as a generating mechanism along with depth for functional box plots to visualize functional data and calculate relevant statistics. The wavelet analysis of variance box plot tool gives competitive error rates in Gaussian test cases with magnitude outliers, and outperforms the functional box plot, for Gaussian test cases with shape outliers. Further, we show wavelet analysis is well suited at approximating irregular and noisy functional data and show the enhanced capability of WANOVA box plots to classify shape outliers which follow a different pattern than other functional data for both simulated and real data instances.