Goodness-of-fit tests for parametric regression models

• 成果类型: Article
• 署名作者: Fan, JQ; Huang, LS
• 署名单位: Chinese University of Hong Kong; University of North Carolina; University of North Carolina Chapel Hill; University of Rochester
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214501753168316
• 发表日期: 2001
• 页码: 640-652
• 关键词: order selection; Nonparametric Regression; smooth test; approximations; difference; variance

摘要

Several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives. These tests formally check if the bias vector of residuals from parametric fts is negligible by using the adaptive Neyman test and other methods. The testing procedures formalize the traditional model diagnostic tools based on residual plots. We examine the rates of contiguous alternatives that can be detected consistently by the adaptive Neyman test. Applications of the procedures to the partially linear models are thoroughly discussed. Our simulation studies show that the new testing procedures are indeed powerful and omnibus. The power of the proposed tests is comparable to the F-test statistic even in the situations where the F test is known to be suitable and can be far more powerful than the F-test statistic in other situations. An application to testing linear models versus additive models is also discussed.