Research On Several Classes Of Semiparametric Empirical Likelihood Test

The semiparametric empirical likelihood method is used wildly in statistics, which combines the semiparametric with empirical likelihood and has advantages as follows:on the one hand, the semiparametric method makes up for parameter model, which the parameter of the regression model has the disadvantage of strong assumptions, and the semiparametric method makes up for nonparametric model, which can’t make full use of the known information; on the other hand, because of the empirical likelihood can be used without the limitations of distribution function, empirical likelihood has advantages in cases which are uncertain or can’t be described with specific function. This dissertation discusses the semiparametric empirical likelihood method based on the multiple change points model and the integral time series.1. According to the same parameter weight function of multiple change points model which contains two change points, we give the semi-parametric empirical likelihood function. The change point estimations and maximum likelihood test statistic of the estimations are given by using Lagrange multiplier. The asymptotic distribution of empirical likelihood ratio test statistic and the p-value of change point estimation are obtained through strong law of large numbers, also we prove that the asymptotic distribution of maximum likelihood function is a continuous and convex function, and the change point estimations obey to three-point distribution. Furthermore, numerical simulation verifies that the semiparametric empirical likelihood test is better than the nonparametric test. The diagnostic of this model with real data set is well.2. The multiple change points model of two change points with weight functions of different parameters is analyzed, the semiparametric empirical likelihood function of proposed model is established by Lagrange multiplier. The change point estimations and p-value of change point estimations are acquired by maximum empirical likelihood estimation, the asymptotic distributions of empirical likelihood ratio and semiparametric empirical likelihood test statistics are given by strong law of large numbers. In simulation, when the location of the true value of change points is in the middle of the random variables, the semiparametric empirical likelihood method is more powerful than nonparametric method, otherwise, the proposed method does not have the superiority. The real data set also verifies the model well.3. The multiple change point of a finite number of multiple change points model with weight functions of different parameters, and the semiparametric empirical likelihood function is constructed. The change point estimations, the p-value of change points,the semiparametric empirical likelihood test statistics and the asymptotic result of the model are obtained by the maximum likelihood function and strong law of large numbers.The bootstrap method which determines the number of change point is simulated, and the result of simulation shows that the proposed semiparametric empirical likelihood method is valid. In the simulation of the accuracy of parameters, the result presents that the semiparametric empirical likelihood method test is better than the nonparametric test when the true value in the middle of the random variables, otherwise, the semiparametric test and the nonparametric test unable to identify the effectiveness. Examples also show that the model fitting is better.4. This dissertation presents the integer valued time series(INAR(k)) model with the occasional level shift random noise, and constructs the semiparametric empirical likelihood function according to dual empirical likelihood. The estimation of parameter is got by Lagrange multiplier. The asymptotic distribution of empirical likelihood ratio test statistic of parameter is Chi-square distribution with the degree of k +2 is proved by strong law of large numbers and central limit theorem, and the confidence interval of parameter is also proved to be a convex set. In addition, the non-occasional level shift random noise influences the model sensitively when the sample size is larger, while the occasional level shift random noise is insignificant.In conclusion, the semiparametric empirical likelihood method has higher efficiency not only in multiple change points model but also in integer valued time series model.This dissertation describes the application of semiparametric empirical likelihood method in the same parameter weight functions model, the different parameters weight functions model, a finite number of change points model, and the integer valued time series model.A large number of numerical simulation experiments and examples are used to prove the effectiveness of the proposed method, and we can see the superiority of semiparametric empirical likelihood method. In a word, the research illustrates that the proposed method is suitable for multiple change points and integer valued time series models.