An integral estimator of residual variance and a measure of explanatory power of covariates in nonparametric regression

Pascal Lavergne; Quang H. Vuong

doi:10.1080/10485259808832750

An integral estimator of residual variance and a measure of explanatory power of covariates in nonparametric regression

Pascal Lavergne, Quang H. Vuong

Research output: Contribution to journal › Article › peer-review

Abstract

We propose a new estimator of unconditional residual variance in nonparametric regression based on the integral of squared residuals. We show its consistency in L¹ under general conditions and derive a nonparametric decomposition of the variance formula. Monte-Carlo experiments suggest that the estimator has good small sample properties.

Original language	English (US)
Pages (from-to)	363-380
Number of pages	18
Journal	Journal of Nonparametric Statistics
Volume	9
Issue number	4
DOIs	https://doi.org/10.1080/10485259808832750
State	Published - 1998

Keywords

Nonparametric R-squared
Residual variance

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1080/10485259808832750

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title = "An integral estimator of residual variance and a measure of explanatory power of covariates in nonparametric regression",

abstract = "We propose a new estimator of unconditional residual variance in nonparametric regression based on the integral of squared residuals. We show its consistency in L1 under general conditions and derive a nonparametric decomposition of the variance formula. Monte-Carlo experiments suggest that the estimator has good small sample properties.",

keywords = "Nonparametric R-squared, Residual variance",

author = "Pascal Lavergne and Vuong, {Quang H.}",

note = "Funding Information: Partial support from the National Science Foundation under grant SBR-9631212 is gratefully acknowledged. We thank an associate editor and two referees for helpful comments that greatly improve our paper.",

year = "1998",

doi = "10.1080/10485259808832750",

language = "English (US)",

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AU - Lavergne, Pascal

AU - Vuong, Quang H.

N1 - Funding Information: Partial support from the National Science Foundation under grant SBR-9631212 is gratefully acknowledged. We thank an associate editor and two referees for helpful comments that greatly improve our paper.

PY - 1998

Y1 - 1998

N2 - We propose a new estimator of unconditional residual variance in nonparametric regression based on the integral of squared residuals. We show its consistency in L1 under general conditions and derive a nonparametric decomposition of the variance formula. Monte-Carlo experiments suggest that the estimator has good small sample properties.

AB - We propose a new estimator of unconditional residual variance in nonparametric regression based on the integral of squared residuals. We show its consistency in L1 under general conditions and derive a nonparametric decomposition of the variance formula. Monte-Carlo experiments suggest that the estimator has good small sample properties.

KW - Nonparametric R-squared

KW - Residual variance

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DO - 10.1080/10485259808832750

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An integral estimator of residual variance and a measure of explanatory power of covariates in nonparametric regression

Abstract

Keywords

ASJC Scopus subject areas

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