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Adaptivity to Local Smoothness and Dimension in Kernel Regression

2020-01-16 | |  63 |   42 |   0

Abstract

We present the first result for kernel regression where the procedure adapts locally at a point x to both the unknown local dimension of the metric space X and the unknown Ho?lder-continuity of the regression function at x. The result holds with high probability simultaneously at all points x in a general metric space X of unknown structure.

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