Tests for Independence in Nonparametric Regression

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

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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
Number of pages19
Publication statusPublished - 2006

Publication series

NameCentER Discussion Paper


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


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