Testing for Polynomial Regression Using Nonparametric Regression Techniques
提出一种基于非参数回归拟合残差的检验方法，用于判断k阶多项式回归模型是否成立，适用于需要验证模型假设的实证研究者。
Abstract In regression analysis, it is important to test the validity of the assumed model prior to making inferences regarding the population of interest. In this investigation, we utilize nonparametric regression techniques to test the validity of a kth order polynomial regression model. The departures from the polynomial model are assumed to belong to a smooth class of functions; a parametric form is not assumed. A test based on nonparametric regression fits to the residuals from kth order polynomial regression is proposed. It utilizes a smoothing spline fit of order 2k to the residuals from kth order polynomial regression. A test statistic based on this estimator is formulated and its asymptotic distribution is derived under alternatives converging to the null at a rate of (nλ¼k )−½, where λ is the smoothing parameter. We note that this rate of convergence is slower than the parametric rate of n −½. Power investigations are conducted through a small-scale simulation study.