Statistical Inference For Quantiles In The Presence Of Auxiliary Information Under Positive Association Samples

Since1967,when Esary et al.introduced the concept of positively associated random variables (r.v.s)into the statistical literature,there has been a signicant number of research papers on this subject matter.Positive association occurs often in certain reliability theory problems,as well as in some important models employed in statistical mechanics. As its wide applications,the convergence and strong consistency of PA random variables were studied extensively.This paper studies statis-tical inference for quantiles in the presence of auxiliary information under PA samples,including point estimation.empirical likelihood confidence interval;and uses the block wise technology into empirical likelihood method,so as to prove the parameters of the logarithm empirical likelihood ratio is asymptotic the chi-square distribution.so we constructed empirical likelihood confidence interval for quantiles in the presence of auxiliary information under PA samples.Here we summary some new findings in this paper:1.We use block wise thechnology into empirical likelihood method.In the article,we according to block wise thechnology to prove the point estimation for quantiles in the presence of auxiliary information under PA samples is asymptotic the normal distribution.2.This paper we use auxiliary information to improve empirical likelihood,contain the loga-rithm of empirical likelihood ratio about quantiles in the presence auxiliary information,and prove it is asymptotic the chi-square distribution and construct the empirical likelihood confidence inter-val.