Nonparametric Test Based On Ranked Set Sampling With Unequal Samples

Ranked set sampling with unequal samples is a sampling protocol that can often beused to improve the cost efficiency of an experiment．It is appropriate for situations inwhich quantification of sampling units is costly or difficult but ranking of the units isinexpensive or easy. Comparing with simple random sampling and ranked set sampling,ranked set sampling with unequal samples can obtain more information about median orsymmetric point using relatively few sample measurements, and the obtained information isvery important to test the population median, the population symmetric point and the twopopulations location parameters. To improve test efficiency and reduce sampling cost asmuch as possible, the nonparametic tests based on ranked set sampling with unequalsamples are researched in this dissertation. The main research parts of this dissertation areas follows:(i) In order to test the median of infinite population, the sign test statistic based onranked set sampling with unequal samples is constructed, its distribution is given and itsasymptotic normality is proved, and its Pitman efficiency factor and efficacy function aregiven. The results of Pitman asymptotic relative efficiency and test efficacy show that theproposed sign test is superior to the sign tests based on simple random sampling and rankedset sampling.(ii) In order to test the median of infinite population, the weighted sign test statisticsbased on ranked set sampling with unequal samples are constructed. Their distributions areshown to be not depend on the population distribution under null hypothesis, and they areshown to have asymptotic normality. The weight vector that maximize the Pitmanefficiency factors of the weighted sign tests is identified, and the optimal weight vector isshown to be distribution-free. The results of Pitman asymptotic relative efficiency andsimulation efficacy show that the optimal weighted sign test based on ranked set samplingwith unequal samples is superior to the optimal weighted sign test based on ranked set sampling.(iii) In order to test the symmetric point of infinite population, the signed-rank teststatistic based on ranked set sampling with unequal samples is constructed, its distributionis shown to be symmetric and not depend on the population distribution under nullhypothesis. The asymptotic normality of the new signed-rank test statistic is proved, and itsPitman efficiency factor is given. The results of Pitman asymptotic relative efficiency andsimulation efficacy show that the proposed signed-rank test is superior to the signed-ranktests based on simple random sampling and ranked set sampling.(iv) In order to test the location parameters of two infinite populations, the rank-sumtest statistic based on ranked set sampling with unequal samples is constructed, itsdistribution is shown to be symmetric and not depend on the population distribution undernull hypothesis. The asymptotic normality of the new rank-sum test statistic is proved, andits Pitman efficiency factor is given. The results of Pitman asymptotic relative efficiencyand simulation efficacy show that the proposed rank-sum test is superior to the rank-sumtests based on simple random sampling and ranked set sampling.The research of this dissertation has important theoretical and practical significance.The research results offer the foundation and idea for interval estimation of the median, theHodges-Lehmann estimation of the location parameter and so on based on ranked setsampling with unequal samples. In addition, the research results have extensive applicationprospect in clinical medicine, environment science, economics and so on.