Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/33542
Title: Testing the significance of index parameters in varying-coefficient single-index models
Authors: Wong, H 
Zhang, R
Leung, B 
Huang, Z
Keywords: χ 2-distribution
Backfitting technique
Generalized F test
Index parameter
Local linear method
Varying-coefficient single-index models
Wilks phenomenon
Issue Date: 2013
Publisher: Elsevier Science Bv
Source: Computational statistics and data analysis, 2013, v. 57, no. 1, p. 297-308 How to cite?
Journal: Computational Statistics and Data Analysis 
Abstract: The varying-coefficient single-index models (VCSIMs) form a class of very flexible and general dimension reduction models, which contain many important regression models such as partially linear models, pure single-index models, partially linear single-index models, varying-coefficient models and so on as special examples. However, the testing problems of the index parameter of the VCSIM have not been very well developed, due partially to the complexity of the models. To this end, based on the estimators obtained by the local linear method and the backfitting technique, we propose the generalized F-type test method to deal with the testing problems of the index parameters of the VCSIM. It is shown that under the null hypothesis the proposed test statistic follows asymptotically a χ2-distribution with the scale constant and the degrees of freedom being independent of the nuisance parameters or functions, which is called the Wilks phenomenon. Simulated data and real data examples are used to illustrate our proposed methodology.
URI: http://hdl.handle.net/10397/33542
ISSN: 0167-9473
DOI: 10.1016/j.csda.2012.07.002
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