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Title: A depth-based global envelope test with applications to biomedical functional data Authors:  Sara Lopez Pintado - Northeastern University (United States) [presenting]
Kun Qian - New York University (United States)
Abstract: Functional data are commonly observed in many emerging biomedical fields and their analysis is an exciting developing area in statistics. The statistical analysis of functions can be significantly improved using non-parametric and robust estimators. New ideas of depth for functional data have been proposed in recent years and can be extended to image data. They provide a way of ordering curves or images from center-outward, and of defining robust order statistics in a functional context. We develop depth-based global envelope tests for comparing two-groups of functions or images. In addition to providing global p-values, the proposed envelope test can be displayed graphically and indicates the specific portion(s) of the functional data (e.g., in pixels or in time) that may have led to the rejection of the null hypothesis. We show in a simulation study the performance of the envelope test in terms of empirical power and size in different scenarios. The proposed depth-based global approach has good power even for small differences and is robust to outliers. The methodology introduced is applied to test whether children with normal and low birth weight have a similar growth pattern. We also analyzed a brain image data set consisting of positron emission tomography (PET) scans of severely depressed patients and healthy controls. The extension of the envelope test to multivariate functional data is explored.