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Abstract:
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Research in many disciplines stands on the analysis of complex high-dimensional data sets. For example, in clinical neuroscience large collections of brain images from different subjects are obtained by advanced scanning techniques to study variations in different neurological states. Developing new tools to analyze the main characteristics of these rich data sets is needed. We consider the basic unit of observation to be a general function, which is defined and takes values in spaces of arbitrary dimension. Based on a notion of depth for general functions denoted multivariate volume depth (MVD), images will be ranked from center-outward and robust estimators can be defined. The theoretical properties of MVD are established and several nonparametric depth-based permutation tests for comparing two groups of images are proposed, in particular, we introduce two-sample location tests based on MVD. In addition, dispersion measures for a sample of images are introduced and used for testing two sample differences in dispersion. All the proposed tests are calibrated in an extensive simulation study. These statistical tools are applied to detect whether there are differences between
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