Abstract
This paper deals with minimax rates of convergence for manifold estimation. A new lower bound is obtained by a novel construction of two sets of manifolds and an application of convex hull testing method of Le Cam (1973). The minimax lower bound matches the upper bound up to a constant factor considered by Genovese et al. (2012b).
Citation
Arlene K. H. Kim. Harrison H. Zhou. "Tight minimax rates for manifold estimation under Hausdorff loss." Electron. J. Statist. 9 (1) 1562 - 1582, 2015. https://doi.org/10.1214/15-EJS1039
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