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.
Bibliographical noteFunding Information:
Lan Wang is Assistant Professor, School of Statistics, University of Minnesota, Minneapolis, MN 55455 (E-mail: firstname.lastname@example.org). Annie Qu is Associate Professor, Statistics Department, Oregon State University, Corvallis, OR 97331 (E-mail: email@example.com). The authors thank two anonymous referees, the associate editor, and the joint editor, whose insightful comments significantly improved the manuscript. The research of Qu was supported in part by the National Science Foundation (grant DMS-03-48764).
- Bounded influence
- Conditional moment test
- Influence function
- Local contamination
- Omnibus alternative
- Robust test