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	Nonparametric inferences for additive models
	Fan, JQ ; Jiang, JC
	2005
关键词	additive models backfitting algorithm generalized likelihood ratio local polynomial regression Wilks phenomenon CENTRAL-LIMIT-THEOREM REGRESSION-MODELS BACKFITTING ESTIMATORS ASYMPTOTIC PROPERTIES SERIES TESTS INTEGRATION ALGORITHM WAVELETS DENSITY
英文摘要	Additive models with backfitting algorithms are popular multivariate nonparametric fitting techniques. However, the inferences of the models have not been very well developed, due partially to the complexity of the backfitting estimators. There are few tools available to answer some important and frequently asked questions, such as whether a specific additive component is significant or admits a certain parametric form. In an attempt to address these issues, we extend the generalized likelihood ratio (GLR) tests to additive models, using the backfitting estimator. We demonstrate that under the null models, the newly proposed GLR statistics follow asymptotically rescaled chi-squared distributions. with the scaling constants and the degrees of freedom independent of the nuisance parameters. This demonstrates that the Wilks phenomenon continues to hold under a variety of smoothing techniques and more relaxed models with unspecified error distributions. We further prove that the GLR tests are asymptotically optimal in terms of rates of convergence for nonparametric hypothesis testing. In addition, for testing a parametric additive model, we propose a bias corrected method to improve the performance of the GLR. The bias-corrected test is shown to share the Wilks type of property. Simulations are conducted to demonstrate the Wilks phenomenon and the power of the proposed tests. A real example is used to illustrate the performance of the testing approach.; Statistics & Probability; SCI(E); 0; ARTICLE; 471; 890-907; 100
语种	英语
出处	SCI
出版者	journal of the american statistical association
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/253088]
专题	数学科学学院
推荐引用方式 GB/T 7714	Fan, JQ,Jiang, JC. Nonparametric inferences for additive models. 2005-01-01.

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