Bernoulli

  • Bernoulli
  • Volume 22, Number 3 (2016), 1729-1744.

Optimal classification and nonparametric regression for functional data

Alexander Meister

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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.

Article information

Source
Bernoulli, Volume 22, Number 3 (2016), 1729-1744.

Dates
Received: April 2014
Revised: December 2014
First available in Project Euclid: 16 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.bj/1458132997

Digital Object Identifier
doi:10.3150/15-BEJ709

Mathematical Reviews number (MathSciNet)
MR3474831

Zentralblatt MATH identifier
1360.62187

Keywords
asymptotic optimality kernel methods minimax convergence rates nonparametric estimation topological data

Citation

Meister, Alexander. Optimal classification and nonparametric regression for functional data. Bernoulli 22 (2016), no. 3, 1729--1744. doi:10.3150/15-BEJ709. https://projecteuclid.org/euclid.bj/1458132997


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