Abstract
Analysis of Variance (ANOVA) for varying coefficient models was investigated in Huang and Chen (2008). In this thesis, we extend their work to construct ANOVA tables and hypothesis tests to examine whether a coefficient function is zero, nonzero constant, and linearity. Based on local polynomial regression, we show that the ANOVA test statistics have asymptotically F-distributions. We compare our ANOVA tests with the GLR tests (Fan and Huang (2005)) by simulations. The numerical results show that the power of the tests are comparable, while the empirical type-I errors are generally smaller than 0.05 for the ANOVA tests, and bigger than 0.05 for the GLR tests. Finally, the proposed tests are used to analyze housing price data in Songshan and Xinyi districts in Taipei city, which leads to some interesting interpretations. The R-code of the proposed ANOVA tests are provided for convenience of applications.