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Title: Confidence regions for filamentary structures Authors:  Wanli Qiao - George Mason University (United States) [presenting]
Abstract: Filamentary structures, also called ridges, generalize the concept of modes of density functions and provide low-dimensional representations of point clouds. Using kernel type plug-in estimators, we give asymptotic confidence regions for filamentary structures based on two bootstrap approaches: multiplier bootstrap and empirical bootstrap. Our theoretical framework differs from many existing ones in the literature in that we allow the possible existence of intersections to emphasize the nontrivial topology of filamentary structures. Our confidence regions are asymptotically valid in different scenarios depending on how flat the filamentary structures are.