With The Statistical Analysis Of The Error Of The Ar (1) Varying Coefficient Models

In recent years, the research of varying-coefficient model attracts considerable attenti-on and becomes an important field in the regression analysis. Varying-coefficient model,useful in many problems especially for econometrics, biomedicine and epidemiology, is anexcellent generalization from linear regression model.This paper discusses the varying-coefficient model with first-order autoregressiveerrors, especially for the method and application of the diagnostics. At first, we obtain theestimation of functional coefficients, the deviation and autoregression coefficients. Whenthe number of case is sufficient, we proved that the functional coefficients' B-splineestimation on thinking over autoregression is better than omitting the autoregression.Then, we get the diagnostic expressions based on case deletion, establish an equivalencebetween the case deletion model and mean shift outlier model. The D-W test and score testare proposed to test the autocorrelation and heteroscedasticity of the random errors invarying-coefficient model. At last, the diagnostic statistic for test outliers and influentialpoint is given. Numerical examples are given to illustrate our results.