Robust tests in regression models with omnibus alternatives and bounded influence

• 成果类型: Article
• 署名作者: Wang, Lan; Qu, Annie
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Oregon State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214506000001130
• 发表日期: 2007
• 页码: 347-358
• 关键词: high breakdown-point; linear-models; hypotheses

摘要

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.