Abstract
In linear models, it is common to test the difference between two nested models by measuring the difference of their error sums of squares and performing an F-test. Huang and Chen (2008) [7] have extended the structure of this F-test to local polynomial regression (LPR) models (see Fan and Gijbels, 1996 [3]), constructed local and global ANOVA decompositions for LPR models, and defined an F-statistic to test whether a model function fitted by LPR is significant. This thesis extends this F-test to multivariate local linear regression (MLLR) models (see Ruppert and Wand, 1994 [17]) by mimicking a similar framework proposed by Huang and Chen (2008) [7]. We establish local and global ANOVA decompositions for MLLR models, and define two F-statistics corresponding to the following two hypotheses: (i) whether a model function fitted by MLLR is significant, and (ii) whether a model function fitted by MLLR with covariates X_2,..., X_d is more appropriate than a model function fitted by MLLR with covariates X_1,..., X_d. In the bivariate case (d = 2), the type I error and power for these two F-tests are investigated by simulations under different settings of sample sizes, correlations of covariates, values of bandwidth, and signals of rejection, while practical issues of implementing these two F-tests are also discussed, including normalization for the product kernel function. At last, these two F-tests are applied to the analysis of Boston house-price data.