| Summary: | 碩士 === 國立清華大學 === 統計學研究所 === 104 === In this paper,we propose an Analysis of Variance (ANOVA) decomposition which separates the contributions from nonparametric and parametric terms for Semiparametric varying coefficient model.
Semiparametric F-test are constructed based on the ANOVA decomposition with the normality assumption. The proposed F-test are applicable to testing whether a coefficient function is zero, a nonzero constant, and linearity. We compare our ANOVA F-test with the generalized likelihood ratio test (GLR) by Fan and Huang (2005) in simulation studies. The two tests are mostly comparable after adjusting their significant levels. Though both the ANOVA F-test and the GLR test are based on local polynomial regression, the proposed test arises from the ANOVA approach and the GLR test from likelihood. Finally, the proposed F-test are used to analyze National Collegiate Athletic Association (NCAA) 2012-2015 basketball data.
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