Abstract
In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.
Highlights
Nonparametric regression model has become one of the main approaches in modern statistics due to its robustness and wide applications
We extend the generalized likelihood ratio test to the varying-coefficient models with censored data
We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a 2 distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon
Summary
Nonparametric regression model has become one of the main approaches in modern statistics due to its robustness and wide applications. In an effort to derive a generally applicable testing approach, Fan et al (2001) proposed the generalized likelihood ratio (GLR) statistic for nonparametric models Fan et al (2001) showed that for a variety of models and a number of nonparametric versus nonparametric and parametric versus nonparametric testing problems, the null distribution of the GLR test statistic follows an asymptotically 2 distribution, independent of nuisance parameters. This property is called the Wilks phenomenon and facilitates the application of the GLR statistic.
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