Abstract:
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With modern high-throughput technologies, scientists can now collect high-dimensional data of various forms, including brain images and medical spectrum curves. These data are featured with high dimension and high correlations in measurement points, making it desirable to find a fast reliable and powerful approach to extract useful information from the wealth of data. This work focuses on improving the power in the testing of high-dimensional functional data. We consider Westfall-Young Randomization Tests in basis-space via lossless or near-lossless compression. We show that these tests satisfy several nice theoretical properties, including the successful control of family-wise error rate, the improving of power with appropriate truncation, and the asymptotic optimality. The effectiveness of this testing approach is demonstrated using two applications - the detection of regions of the spectrum that are related to pre-cancer using fluorescence spectroscopy data and the detection of disease-related regions using fluorescence spectroscopy data and the detection of disease-related regions using Tensor-Based Morphometry data derived from structural magnetic resonance imaging.
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