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Second-Order Comparison of Functional Data with Applications to DNA Geom

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Given two samples of continuous random curves, we consider the problem of comparing their smoothness properties as these are encoded by their covariance structure. Our study is motivated by the problem of determining whether the mechanical properties of short strands of DNA are significantly affected by their base-pair sequence; while this is believed to be true, it has not been confirmed by 3D data. The corresponding functional testing problem is seen to involve aspects of ill-posed inverse problems and a test based on spectral truncation is proposed and investigated. More generally, we introduce the notion of a dispersion operator as a descriptor of second-order functional properties and consider the problem of comparing the dispersion operators of two functional populations. When applied to a dataset of DNA minicircles obtained through the electron microscope, our tests seems to suggest the existence of a sequence effect on DNA shape.

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