Testing the Goodness of Fit of a Linear Model Via Nonparametric Regression Techniques
本文研究用非参数回归方法检验线性模型是否合适，提出基于残差的新检验统计量，证明其能检测固定替代假设但无法检测以参数速度收敛的局部替代，模拟显示基于三次平滑样条的检验有良好功效。
Abstract This article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model. The large-sample properties of parametric goodness-of-fit tests for linearity are considered. The inadequacies of such tests lead to the proposal of new tests that are constructed from nonparametric regression fits to the residuals from linear regression. Large-sample theory is derived for two variants of this type of statistic. The results demonstrate that such tests are consistent against all fixed smooth alternatives to linearity but are incapable of detecting local alternatives converging to a linear model at the parametric rate n −1/2. Simulation experiments involving a test based on fitting cubic smoothing splines to residuals reveals that this test has good power properties against several reasonable alternatives