- Volume 22, Number 3 (2016), 1729-1744.
Optimal classification and nonparametric regression for functional data
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.
Bernoulli, Volume 22, Number 3 (2016), 1729-1744.
Received: April 2014
Revised: December 2014
First available in Project Euclid: 16 March 2016
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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