Empirical Likelihood For Nonlinear Semiparametric Models With M-dependent Errors

The empirical likelihood method as an nonparametric confidence interval and testing meyhods is an important method. Owenstudied the general nature of this method systematically. Many research results indicate that the empirical likelihood method has the good nature simiar to the bootstrap. There are many outstanding advantages of the approach compared to the classic or modern statistical methods, such as:in addition to using empirical likelihood method to construct confidence interval has the advantages of the transformation invariance, the domain preservation and the shape of the confidence region decided by the data, etc. The approach also has the advantages of Bartlett correction and there is no need to construst axis of statistics and so on. Thus empirical likelihood method has become the focus of the statistics. Later, people find out that empirical likelihood approach is effective and adaptable, and thus such a powerful statistical tool has been extended to a wider range of statistical models.In this paper, empirical likelihood for nonlinear semiparametric models with m-denpendent errors studied based on Qin Y S et aland Feng et al.In the first chapter, the backgrounds and recent researchs of the empirical likelihood method are introduced, and given some Lemmas and Theorems by Owen.In the second chapter, by m-dependent sequence of nature has achieved results, we use the empirical likelihood method to discuss the unknown parametric statistic inference problem of nonlinear semiparametric models(2.1) under m-dependent errors. When the parametricβis ture, given the empirical likelihood inference ofβ.and shown asymptotically distributde of empirical likelihood ratio statistics ofβ. We use blockwise empirical likelihood method, which demonstrates that the proposed statistic submit to chi-square distribution. by the result, we can construct the confidence regions of unknown parameter.