Empirical Likelihood Inference Of Nonlinear Varying-coefficient Models

As the most commonly used statistical technique, regression analysis has been utilized to explore the association between dependent and independent variables and further to identify how independent variables impact the dependent variable. This paper use the empirical likelihood method to study the nonlinear Varying-coefficient models.Empirical likelihood method, the highly attention method, is a non-parametric statistical method. Compared with traditional asymptotic normality method, using empirical likelihood method to construct confidence region of parameters don’t need to estimate the asymptotic variance, it is an advantage of the empirical likelihood method. Compared with traditional asymptotic normality method, the accuracy of the estimated of empirical likelihood method is higher and the interval length shorter, the more important is that the confidence region of the shape can be automatically determined by the data. Many statisticians have applied this method to a variety of statistical models, such as linear model, partly linear model, nonlinear model, etc. For the nonlinear Varying-coefficient models haven’t seen relevant literature.This paper investigates the question of the nonlinear Varying-coefficient models using empirical likelihood method. Then construct the empirical log-likelihood ratio statistic and adjusted empirical log-likelihood ratio statistic for unknown coefficient function. Under certain conditions, proves that the empirical log-likelihood ratio follows an asymptotically 2? distribution, and constructs a confidence region of the unknown coefficient function. In addition, this chapter constructs least squares estimators of the unknown coefficient function and proves its asymptotic properties. Then, combining with the R software, study the simulation of one classic nonlinear varying-coefficient models. By corresponding simulation results, at the coverage probability and accuracy of confidence region, the empirical likelihood method is better than the least squares method. At the last of this paper, we give out proves of some main results.