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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert


Cite Score 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.354
Source Normalized Impact per Paper (SNIP) 2018: 0.604

Mathematical Citation Quotient (MCQ) 2018: 0.36

Online
ISSN
2196-7040
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Volume 30, Issue 1

Issues

Rate of convergence of the density estimation of regression residual

László Györfi / Harro Walk
Published Online: 2013-03-06 | DOI: https://doi.org/10.1524/strm.2013.1127

Abstract

Consider the regression problem with a response variable Y and with a d-dimensional feature vector X. For the regression function m(x) = E{Y|X = x}, this paper investigates methods for estimating the density of the residual Y − m(X) from independent and identically distributed data. If the density is twice differentiable and has compact support then we bound the rate of convergence of the kernel density estimate. It turns out that for d ≤ 3 and for partitioning regression estimates, the regression estimation error has no influence on the rate of convergence of the density estimate.

Keywords: regression residual; kernel density estimation; partitioning; kernel and nearest neighbor regression estimation; rate of convergence.

About the article

* Correspondence address: Budapest University of Technology and Economics, Dept. of Computer Science and Information Theory, 1521 Stoczek u. 2, Budapest, Ungarn,


Published Online: 2013-03-06

Published in Print: 2013-03-01


Citation Information: Statistics & Risk Modeling with Applications in Finance and Insurance, Volume 30, Issue 1, Pages 55–74, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1524/strm.2013.1127.

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