### 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.

Original language | English |
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Pages (from-to) | 55-74 |

Number of pages | 20 |

Journal | Statistics and Risk Modeling |

Volume | 30 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2013 |

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### Keywords

- kernel and nearest neighbor regression estimation
- kernel density estimation
- partitioning
- rate of convergence
- Regression residual

### ASJC Scopus subject areas

- Statistics and Probability
- Modelling and Simulation
- Statistics, Probability and Uncertainty

### Cite this

*Statistics and Risk Modeling*,

*30*(1), 55-74. https://doi.org/10.1524/strm.2013.1127

**Rate of convergence of the density estimation of regression residual.** / Györfi, L.; Walk, Harro.

Research output: Contribution to journal › Article

*Statistics and Risk Modeling*, vol. 30, no. 1, pp. 55-74. https://doi.org/10.1524/strm.2013.1127

}

TY - JOUR

T1 - Rate of convergence of the density estimation of regression residual

AU - Györfi, L.

AU - Walk, Harro

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

KW - kernel and nearest neighbor regression estimation

KW - kernel density estimation

KW - partitioning

KW - rate of convergence

KW - Regression residual

UR - http://www.scopus.com/inward/record.url?scp=84884958573&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884958573&partnerID=8YFLogxK

U2 - 10.1524/strm.2013.1127

DO - 10.1524/strm.2013.1127

M3 - Article

AN - SCOPUS:84884958573

VL - 30

SP - 55

EP - 74

JO - Statistics and Risk Modeling

JF - Statistics and Risk Modeling

SN - 2193-1402

IS - 1

ER -