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Biometrika 2009 96(1):133-148; doi:10.1093/biomet/asn074
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© 2009 Biometrika Trust

Articles

Model checking in regression via dimension reduction

Yingcun Xia

Department of Statistics and Applied Probability, National University of Singapore, 117546, Singapore staxyc{at}stat.nus.edu.sg

Received for publication 1 December 2006. Revision received 1 March 2008.
  Abstract

Lack-of-fit checking for parametric and semiparametric models is essential in reducing misspecification. The efficiency of most existing model-checking methods drops rapidly as the dimension of the covariates increases. We propose to check a model by projecting the fitted residuals along a direction that adapts to the systematic departure of the residuals from the desired pattern. Consistency of the method is proved for parametric and semiparametric regression models. A bootstrap implementation is also discussed. Simulation comparisons with several existing methods are made, suggesting that the proposed methods are more efficient than the existing methods when the dimension increases. Air pollution data from Chicago are used to illustrate the procedure.

Key Words: Bootstrap • Crossvalidation • Goodness-of-fit • Kernel smoothing • Semiparametric model • Single-index model


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