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August 2016 Optimal classification and nonparametric regression for functional data
Alexander Meister
Bernoulli 22(3): 1729-1744 (August 2016). DOI: 10.3150/15-BEJ709

Abstract

We establish minimax convergence rates for classification of functional data and for nonparametric regression with functional design variables. The optimal rates are of logarithmic type under smoothness constraints on the functional density and the regression mapping, respectively. These asymptotic properties are attainable by conventional kernel procedures. The bandwidth selector does not require knowledge of the smoothness level of the target mapping. In this work, the functional data are considered as realisations of random variables which take their values in a general Polish metric space. We impose certain metric entropy constraints on this space; but no algebraic properties are required.

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Alexander Meister. "Optimal classification and nonparametric regression for functional data." Bernoulli 22 (3) 1729 - 1744, August 2016. https://doi.org/10.3150/15-BEJ709

Information

Received: 1 April 2014; Revised: 1 December 2014; Published: August 2016
First available in Project Euclid: 16 March 2016

zbMATH: 1360.62187
MathSciNet: MR3474831
Digital Object Identifier: 10.3150/15-BEJ709

Keywords: asymptotic optimality , kernel methods , Minimax convergence rates , nonparametric estimation , topological data

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

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Vol.22 • No. 3 • August 2016
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