Testing linear regression relationships via locally-weighted fitting technique.(Chinese. English summary)Zbl 1024.62029

Summary: This article investigates the use of locally-weighted fitting techniques to test for linearity of a regression relationship. An appropriate test statistic is constructed based on the residual sums of squares after fitting the linear and varying-parameter models. A procedure for computing the exact $$p$$-value of the test is proposed. For computational consideration in practice, a method to approximate the $$p$$-value is derived by employing the three-moment $$\chi^2$$ approximation. Simulations and analysis of a practical problem demonstrate that the three-moment $$\chi^2$$ approximation is rather accurate in approximating the null distribution of the statistics, and the proposed test is satisfactorily powerful in exploring nonlinearity of a regression function.

MSC:

 62J02 General nonlinear regression 62G08 Nonparametric regression and quantile regression