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Title: Generalized likelihood ratio test for varying-coefficient models with different smoothing variables
Authors: Ip, WC
Wong, H 
Zhang, R
Keywords: Different smoothing variables
Efficient estimator
Generalized likelihood ratio test
Varying-coefficient models
Wilks phenomenon
Issue Date: 2007
Publisher: Elsevier
Source: Computational statistics and data analysis, 2007, v. 51, no. 9, p. 4543-4561 How to cite?
Journal: Computational Statistics and Data Analysis 
Abstract: Varying-coefficient models are popular multivariate nonparametric fitting techniques. When all coefficient functions in a varying-coefficient model share the same smoothing variable, inference tools available include the F-test, the sieve empirical likelihood ratio test and the generalized likelihood ratio (GLR) test. However, when the coefficient functions have different smoothing variables, these tools cannot be used directly to make inferences on the model because of the differences in the process of estimating the functions. In this paper, the GLR test is extended to models of the latter case by the efficient estimators of these coefficient functions. Under the null hypothesis the new proposed GLR test follows the χ2-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Further, we have derived its asymptotic power which is shown to achieve the optimal rate of convergence for nonparametric hypothesis testing. A simulation study is conducted to evaluate the test procedure empirically.
DOI: 10.1016/j.csda.2006.07.027
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