Empirical Likelihood Inference For Population Quantiles In The Presence Of Auxiliary Information Under α-mixing Sample

The α-mixing condition was firstly introduced by Rosenblatt in 1956.The limit theory of a-mixing sequence is discussed in detail by Lu Chuanrong and Lin Zhengyan (1997).In order to constructing confidence intervals of interested Parameters, Owen(1998,1990) proposed the em-pirical likelihood method, which has many advantages over its counterparts, like the normal-approximation-based method.This paper mainly studies empirical likelihood inference for population quantiles in the pres-ence of auxiliary information under α-mixing samples, and uses the blockwise technology into empirical likelihood method, which was proposed by Kitamurac(1997). It is shown that the pro-posed quantile estimators are asymptotically normally distributed, so as to prove the paramerers of the logarithm empirical likelihood ratio is asymptotic the chi-square distribution, so we constructed empirical likelihood confidence interval for population quantiles in the presence of auxiliary in-formation under α-mixing samples. We also consider a hypothesis testing on the basis of the research.Here we summary some new findings in this paper:1. This paper we study the asymptotic distribution for population quantiles in the presence of auxiliary information under α-mixing samples, and use auxiliary information to improve empirical likelihood. It’s shown that the proposed quantile estimators are asymptotically normally distributed with smaller asymptotic variances than those of the usual quantile estimators.2. This paper we study the asymptotic properties of estimation and the construction of confi-dence intervals for population quantiles in the presence of auxiliary information under α-mixing samples by using the blockwise technique, and prove the paramerers of the logarithm empirical likelihood ratio is asymptotic the chi-square distribution. It’s shown that the empirical likelihood confidence interval length of population quantiles in the presence of auxiliary information is more smaller than the one in the absence of auxiliary information.3. For testing a hypothesis about the population quantiles, the power of a test statistic in the presence of auxiliary information is lager than the one in the absence of auxiliary information, and the power of a test statistic is not reduced when the amount of information increased.