A joint test for parametric specification and independence in nonlinear regression models
提出一种同时检验非线性回归模型中误差与解释变量独立性以及回归函数参数设定的方法，适用于同方差和异方差情形，并通过模拟和实例验证了有效性。
This paper develops a testing procedure to simultaneously check (i) the independence between the error and the regressor(s), and (ii) the parametric specification in nonlinear regression models. This procedure generalizes the existing work of Sen and Sen [“Testing Independence and Goodness-of-fit in Linear Models,” Biometrika, 101, 927–942.] to a regression setting that allows any smooth parametric form of the regression function. We establish asymptotic theory for the test procedure under both conditional homoscedastic error and heteroscedastic error. The derived tests are easily implementable, asymptotically normal, and consistent against a large class of fixed alternatives. Besides, the local power performance is investigated. To calibrate the finite sample distribution of the test statistics, a smooth bootstrap procedure is proposed and found work well in simulation studies. Finally, two real data examples are analyzed to illustrate the practical merit of our proposed tests.