Generalized likelihood ratio test for varying-coefficient models with different smoothing variables |
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Authors: | Wai-Cheung Ip Heung Wong |
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Affiliation: | a Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong b Department of Statistics, East China Normal University, PR China |
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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. |
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Keywords: | Different smoothing variables Efficient estimator Generalized likelihood ratio test Varying-coefficient models Wilks phenomenon |
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