Applying Backward Nested Subspace Inference to Tori and Polyspheres

07/11/2017
Publication GSI2017
OAI : oai:www.see.asso.fr:17410:22521
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For data with non-Euclidean geometric structure, hypothesis testing is challenging because most statistical tools, for example principal component analysis (PCA), are specific for linear data with a Euclidean structure. In the last 15 years, the subject has advanced through the emerging development of central limit theorems, first for generalizations of means, then also for geodesics and more generally for lower dimensional subspaces. Notably, there are data spaces, even geometrically very benign, such as the torus, where this approach is statistically not feasible, unless the geometry is changed, to that of a sphere, say. This geometry is statistically so benign that nestedness of Euclidean PCA, which is usually not given for the above general approaches, is also naturally given through principal nested great spheres (PNGS) and even more flexible than Euclidean PCA through  principal nested (small) spheres (PNS). In this contribution we illustrate applications of bootstrap two-sample tests for the torus and its higher dimensional generalizations, polyspheres.

Applying Backward Nested Subspace Inference to Tori and Polyspheres

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application/pdf Applying Backward Nested Subspace Inference to Tori and Polyspheres Benjamin Eltzner, Stephan Huckemann
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contenu protégé  Document accessible sous conditions - vous devez vous connecter ou vous enregistrer pour accéder à ou acquérir ce document.
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For data with non-Euclidean geometric structure, hypothesis testing is challenging because most statistical tools, for example principal component analysis (PCA), are specific for linear data with a Euclidean structure. In the last 15 years, the subject has advanced through the emerging development of central limit theorems, first for generalizations of means, then also for geodesics and more generally for lower dimensional subspaces. Notably, there are data spaces, even geometrically very benign, such as the torus, where this approach is statistically not feasible, unless the geometry is changed, to that of a sphere, say. This geometry is statistically so benign that nestedness of Euclidean PCA, which is usually not given for the above general approaches, is also naturally given through principal nested great spheres (PNGS) and even more flexible than Euclidean PCA through  principal nested (small) spheres (PNS). In this contribution we illustrate applications of bootstrap two-sample tests for the torus and its higher dimensional generalizations, polyspheres.
Applying Backward Nested Subspace Inference to Tori and Polyspheres
application/pdf Applying Backward Nested Subspace Inference to Tori and Polyspheres

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