Joint Confidence Regions For A Finite Number Of Quantiles Under φ-mixing Samples

This thesis investigates asymptotic properties for the kernel estimator of a finite num-ber quantiles of a population under φ-mixing samples and the joint empirical likelihood confidence regions for a finite number quantiles.The first chapter is introduction. We introduce survey of φ-mixing, research progress of the empirical likelihood method, research progress of the kernel estimator of quantile and the research content and innovation points.The second chapter studies asymptotic properties for the kernel estimator of a finite number quantiles of a population under φ-mixing samples. It is proved the kernel esti-mator of a finite number quantiles of a population under φ-mixing samples is asymptotic normal distribution by using Lyapunov central limit theorem and the blockwise tech-nique. On the basis of this, it analysis asymptotic properties for the kernel estimator of a finite number quantiles of a population under φ-mixing samples. It is shown that the kernel estimator of a finite number quantiles of a population under φ-mixing samples is asymptotically multivariate normal distribution.The third chapter studies empirical likelihood confidence intervals for a finite num-ber of quantiles of a population under φ-mixing samples. First we construct the block empirical likelihood ratio statistics by the empirical likelihood method. Then is found that the blockwise empirical likelihood (EL) ratio statistic is asymptotically chi-square distributed by using the blockwise technique. The result is used to obtain EL-based con-fidence interval for a finite number of quantiles under0-mixing samples. The empirical likelihood confidence intervals for the difference of two quantiles is also developed.The innovation of this paper is mainly reflected in the following three aspects:1、It analysis the asymptotic properties for the kernel estimator of finite number quantiles of the population under0-mixing samples and the quantile estimation is asymp-totically normal distributed from a single point to multi point.2、It studied EL-based the properties of blockwise empirical likelihood ratio statis-tics for a finite number of quantiles under φ-mixing samples, and it is proved that the blockwise empirical likelihood (EL) ratio statistic is x2distributed. The result is used to obtain EL-based confidence interval for a finite number of quantiles under0-mixing samples.3、It employ EL-based confidence interval for a finite number of quantiles to con-structs empirical likelihood confidence intervals for difference of two quantiles of popula-tion under φ-mixing samples.