Robust tests in regression models with omnibus alternatives and bounded influence

Lan Wang, Annie Qu

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

A robust approach for testing the parametric form of a regression function versus an omnibus alternative is introduced. This generalizes existing robust methods for testing subhypotheses in a regression model. The new test is motivated by developments in modern smoothing-based testing procedures and can be viewed as a robustification of a smoothing-based conditional moment test. It is asymptotically normal under both the null hypothesis and local alternatives. The robustified test retains the "omnibus" property of the corresponding smoothing test; that is, it is consistent for any fixed smooth alternative in an infinite-dimensional space. It is shown that the bias of the asymptotic level under shrinking local contamination is bounded only if the second-order Hampel's influence function is bounded. The test's performance is demonstrated through both Monte Carlo simulations and application to an agricultural dataset.

Original languageEnglish (US)
Pages (from-to)347-358
Number of pages12
JournalJournal of the American Statistical Association
Volume102
Issue number477
DOIs
StatePublished - Mar 1 2007

Keywords

  • Bounded influence
  • Conditional moment test
  • Influence function
  • Local contamination
  • Omnibus alternative
  • Regression
  • Robust test
  • Smoothing

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