Empirical Likelihood Inference For Linear Models Based On Dependent Errors

The data gathered from study of some modern sciences such as biology and information science is usually large, high dimensional and dependent. This is one of the most popular, most challenging domains and is most likely to be broken through in applications and theories of statistics. So, the studies for dependent data has aroused people's attention. The studies, however, for statistical models based on dependent data is still insufficient and not much accounted of. This paper investigate a linear model which is based on two kinds dependent errors, one is martingale difference process and another is sub-stable linear process.For the parameter β, there is usually least square method in literatures.In this paper, we present a new way-empirical likelihood inference to treat the model. Empirical likelihood method has many advantages. For example, the confidence intervals constructed has invariablity, the shapes of confidence regions are all determined by their data and Bartlett-Correctable, and so on. So this method is very significative in both theories and applications.First of all, we adopt empirical likelihood to the linear model based on martingale difference errors, construct empirical log-likelihood ratio statistic of the parameter and we prove that the empirical log-likelihood ratio statistic is asymptotically chi-squared distributed under quite general conditions. Second,...