Goodness-of-fit diagnostics for regression models
针对固定设计回归模型，提出一种基于核估计的拟合优度检验方法，通过数据自适应带宽选择避免主观性，检验统计量渐近服从卡方分布，适用于参数模型是否正确的诊断。
For a fixed design regression model, we compare the fitting of parametric linear or non-linear models by the least squares method with a model-free non-parametric approach via kernel estimates. One major problem for such a comparison is the necessary bandwidth choice for the non-parametric estimate, and a data-adaptive method for local bandwidth choice based on the parametric fit is proposed. As an application, we consider comparison of both estimates and of corresponding estimates of derivatives at a finite number of preselected points. This leads to a test statistic which is asymptotically x2 distributed under the null hypothesis that the parametric model contains the underlying regression function g and has asymptotic power 1 under certain contiguous alternatives. As compared to other proposed goodness-of-fit procedures, this test does not depend on the subjective choice of a bandwidth. Practical issues and diagnostic plots are illustrated in a data application.