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Asymptotic analysis of quantile regression learning based on coefficient dependent regularization

School of Mathematical Sciences, University of Jinan, Jinan 250022, P. R. China

and

School of Mathematical Sciences, University of Jinan, Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Jinan 250022, P. R. China

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https://doi.org/10.1142/S0219691315500186Cited by:7 (Source: Crossref)

Abstract

In this paper, we consider conditional quantile regression learning algorithms based on the pinball loss with data dependent hypothesis space and ℓ²-regularizer. Functions in this hypothesis space are linear combination of basis functions generated by a kernel function and sample data. The only conditions imposed on the kernel function are the continuity and boundedness which are pretty weak. Our main goal is to study the consistency of this regularized quantile regression learning. By concentration inequality with ℓ²-empirical covering numbers and operator decomposition techniques, satisfied error bounds and convergence rates are explicitly derived.

Keywords:

AMSC: 22E46, 53C35, 57S20

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