Tests for Independence in Nonparametric Regression

J.H.J. Einmahl, I. van Keilegom

Research output: Working paperDiscussion paperOther research output

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Abstract

Consider the nonparametric regression model Y = m(X)+e, where the function m is smooth, but unknown.We construct tests for the independence of e and X, based on n independent copies of (X; Y ).The testing procedures are based on differences of neighboring Y 's.We establish asymptotic results for the proposed tests statistics, investigate their finite sample properties through a simulation study and present an econometric application to household data.The proofs are based on delicate empirical process theory.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages19
Volume2006-80
Publication statusPublished - 2006

Publication series

NameCentER Discussion Paper
Volume2006-80

Fingerprint

M-function
Empirical Process
Nonparametric Model
Nonparametric Regression
Econometrics
Test Statistic
Regression Model
Simulation Study
Unknown
Testing
Independence

Keywords

  • empirical process
  • model diagnostics
  • nonparametric regression
  • test for independence
  • weak convergence

Cite this

Einmahl, J. H. J., & van Keilegom, I. (2006). Tests for Independence in Nonparametric Regression. (CentER Discussion Paper; Vol. 2006-80). Tilburg: Econometrics.
Einmahl, J.H.J. ; van Keilegom, I. / Tests for Independence in Nonparametric Regression. Tilburg : Econometrics, 2006. (CentER Discussion Paper).
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series = "CentER Discussion Paper",
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Einmahl, JHJ & van Keilegom, I 2006 'Tests for Independence in Nonparametric Regression' CentER Discussion Paper, vol. 2006-80, Econometrics, Tilburg.

Tests for Independence in Nonparametric Regression. / Einmahl, J.H.J.; van Keilegom, I.

Tilburg : Econometrics, 2006. (CentER Discussion Paper; Vol. 2006-80).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Tests for Independence in Nonparametric Regression

AU - Einmahl, J.H.J.

AU - van Keilegom, I.

N1 - Subsequently published in Statistica Sinica, 2008 Pagination: 19

PY - 2006

Y1 - 2006

N2 - Consider the nonparametric regression model Y = m(X)+e, where the function m is smooth, but unknown.We construct tests for the independence of e and X, based on n independent copies of (X; Y ).The testing procedures are based on differences of neighboring Y 's.We establish asymptotic results for the proposed tests statistics, investigate their finite sample properties through a simulation study and present an econometric application to household data.The proofs are based on delicate empirical process theory.

AB - Consider the nonparametric regression model Y = m(X)+e, where the function m is smooth, but unknown.We construct tests for the independence of e and X, based on n independent copies of (X; Y ).The testing procedures are based on differences of neighboring Y 's.We establish asymptotic results for the proposed tests statistics, investigate their finite sample properties through a simulation study and present an econometric application to household data.The proofs are based on delicate empirical process theory.

KW - empirical process

KW - model diagnostics

KW - nonparametric regression

KW - test for independence

KW - weak convergence

M3 - Discussion paper

VL - 2006-80

T3 - CentER Discussion Paper

BT - Tests for Independence in Nonparametric Regression

PB - Econometrics

CY - Tilburg

ER -

Einmahl JHJ, van Keilegom I. Tests for Independence in Nonparametric Regression. Tilburg: Econometrics. 2006. (CentER Discussion Paper).