Ranked-set sampling(RSS) often provides more efficient inference than simple random sampling(SRS).In this article,we propose a systematic nonparametric technique,RSS-EL,for hypoth-esis testing and interval estimation with balanced RSS data using empirical likelihood(EL).We detail the approach for interval estimation and hypothesis testing in one-sample and two-sample problems and general estimating equations.In all three cases,RSS is shown to provide more efficient inference than SRS of the same size.Moreover,the RSS-EL method does not require any easily violated assumptions needed by existing rank-based nonparametric methods for RSS data,such as perfect ranking,identical ranking scheme in two groups,and location shift between two population distributions.The merit of the RSS-EL method is also demonstrated through simulation studies.
Dempster and Rubin(D&R) in their JRSSB paper considered the statistical error caused by data rounding in a linear regression model and compared the Sheppard correction,BRB correction and the ordinary LSE by simulations.Some asymptotic results when the rounding scale tends to 0 were also presented.In a previous research,we found that the ordinary sample variance of rounded data from normal populations is always inconsistent while the sample mean of rounded data is consistent if and only if the true mean is a multiple of the half rounding scale.In the light of these results,in this paper we further investigate the rounding errors in linear regressions.We notice that these results form the basic reasons that the Sheppard corrections perform better than other methods in D&R examples and their conclusion in general cases is incorrect.Examples in which the Sheppard correction works worse than the BRB correction are also given.Furthermore,we propose a new approach to estimate the parameters,called "two-stage estimator",and establish the consistency and asymptotic normality of the new estimators.
LIU TianQing1,ZHANG BaoXue1,HU GuoRong1 & BAI ZhiDong1,2,1Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China
