Empirical Likelihood Inference Of Parameters In A Semi-parametric Varying-coefficient Partially Linear EV Models

Empirical likelihood for constructing the confidence region is a nonparametric method of inference introduced by Owen (1988,1990), has many advantages, as widely attention. For example, using empirical likelihood method to construct confidence interval don’t need to estimate the asymptotic variance, 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, nonparametric model, semi-parametric model, etc.In practical applications often due to some reason the data cannot be precisely observed with measurement error, however some statisticians apply empirical likelihood method to the model with measurement error. Such as Wang (2009), Hu (2007), etc use the empirical likelihood method to study the semi-parametric varying-coefficient partially linear model which the part of parameters with measurement error. Feng (2012), etc use the empirical likelihood method to study the semi-parametric varying-coefficient partially linear model which the part of nonparametric with measurement error. For the semi-parametric varying-coefficient partially linear model which both the parameter and the nonparametric part with measurement error haven’t seen relevant literatures.The paper consists of the following four chapters:Chapter1mainly introduces the general form of partially linear varying-coefficient EV model, introduces the local polynomial estimation method which to estimate the parameters of the model and the empirical likelihood method which used to construct the parameters confidence interval.Chapter2use the local polynomial estimation method to give the parameter estimates, constructs the logarithmic empirical likelihood function of the unknown parameters Under certain conditions the empirical likelihood ratio function asymptotic convergence χ2as well as the estimation of parameters β and function α(·) is asymptotic normality.Chapter3by numerical simulations in the situation of limited samples, studys the actual performance of the proposed conclusions. Chapter4gives the theorem proof process in this paper, and applies Cauchy-Schwarzinequality, Slutsky theorem, law of large Numbers and central-limit theorem etc.