Model diagnosis for parametric regression in high-dimensional spaces

W. Stute*, W. L. Xu, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)

Abstract

We study tools for checking the validity of a parametric regression model. When the dimension of the regressors is large, many of the existing tests face the curse of dimensionality or require some ordering of the data. Our tests are based on the residual empirical process marked by proper functions of the regressors. They are able to detect local alternatives converging to the null at parametric rates. Parametric and nonparametric alternatives are considered. In the latter case, through a proper principal component decomposition, we are able to derive smooth directional tests which are asymptotically distribution-free under the null model. The new tests take into account precisely the 'geometry of the model'. A simulation study is carried through and an application to a real dataset is illustrated.

Original languageEnglish
Pages (from-to)451-467
Number of pages17
JournalBiometrika
Volume95
Issue number2
DOIs
Publication statusPublished - Jun 2008

Scopus Subject Areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

User-Defined Keywords

  • Marked residual empirical process
  • Model check
  • Principal components

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