The Empirical Euclidean Likelihood Inference For Linear Model Under Right Censored Data

Empirical likelihood method is a kind of statistical method, it has many excellent statistical properties, such as the shape of the empirical likelihood area only related to the sample, parameter estimation with consistency, em-pirical likelihood statistics converge to chi-square distribution, etc. In recent years, many statistics apply this method to different types of data and models. However, the compute of empirical likelihood is complicate. Owen (1991) pro-posed the Empirical Euclidean likelihood method firstlly, the method is that using Euclidean distance instead of likelihood distance. It has been proved that it’s large sample properties are analogous to empirical Likelihood’s, so that this method has higher theoretical significance and application value.In this thesis, we are mainly focus on the application of the empirical Eu-clidean likelihood to linear model under the right censored data, an empirical Euclidean likelihood statistic and a adjusted empirical Euclidean likelihood s-tatistic are constructed in this case, the limiting distributions of these statistics are obtained, thereby to construct confidence region for the regression param-eter. In the simulation results also show the confidence region constructed by adjusted Euclidean likelihood is superior to the traditional normal asymptotic method’s. This master s degree thesis consist of four chapers.In first chapter, we recall some basic backgrounds of the empirical Eu-clidean likelihood and list the main results of the thesis.In second chapter, we present some basic definitions and conclusions of the empirical Euclidean likelihood needed in the sequel.In third chapter, firstly, we introduce an estimation method of the pa-rameter in linear model with the right censored data, and we construct an em-pirical Euclidean likelihood statistic and a adjusted empirical Euclidean like-lihood statistic. Then, we conclude that the empirical Euclidean likelihood ratio statistics converge to noncentral chi-square distribution and the adjust the empirical Euclidean likelihood ratio statistics converge to center chi-square distribution,and by these facts, we get the confidence region for the regression parameter. Finally, the ajusted empirical Euclidean likelihood with additional information is discussed.In fourth chapter, we do a simulation research under the method pro-posed in third chapter, and the simulation results show that in the case of the censored rate is not too high the coverage of the confidence region construct-ed by the empirical Euclidean likelihood and the adjusted empirical Euclidean likelihood method are higher than that by the normal approximation method.