{"title":"On the problems of PPS sampling in multi-character surveys","authors":"A. C. Akpanta","doi":"10.4314/gjmas.v8i1.50812","DOIUrl":null,"url":null,"abstract":"This paper, which is on the problems of PPS sampling in multi-character surveys, compares the efficiency of some estimators used in PPSWR sampling for multiple characteristics. From a superpopulation model, we computed the expected variances of the different estimators for each of the first two finite populations considered, as well as the exact bias and variance of each of these estimators. The results obtained show that the estimators proposed by Rao (1966), Amahia et. al. (1989) and the alternative in Amahia et. al. (1989) are better than the conventional estimator. In population I, where the study variable and the ancillary variable are highly and positively correlated, results show that the estimator in Amahia et. al. (1989) fare better than the alternative estimator. On the other hand, the results obtained from our population II where the correlation between the study variable and the ancillary variable is poor, reveal that the alternative estimator in Amahia et. al. (1989) is more efficient. Several other finite populations whose ρare neither too high as in population I nor too poor as in population II were considered and it was discovered that the competition for efficiency only rests with the two estimators suggested by Amahia et al (1989) and Rao (1966). These interesting comparative results are shown in Tables.","PeriodicalId":126381,"journal":{"name":"Global Journal of Mathematical Sciences","volume":"6 8","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Global Journal of Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4314/gjmas.v8i1.50812","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
This paper, which is on the problems of PPS sampling in multi-character surveys, compares the efficiency of some estimators used in PPSWR sampling for multiple characteristics. From a superpopulation model, we computed the expected variances of the different estimators for each of the first two finite populations considered, as well as the exact bias and variance of each of these estimators. The results obtained show that the estimators proposed by Rao (1966), Amahia et. al. (1989) and the alternative in Amahia et. al. (1989) are better than the conventional estimator. In population I, where the study variable and the ancillary variable are highly and positively correlated, results show that the estimator in Amahia et. al. (1989) fare better than the alternative estimator. On the other hand, the results obtained from our population II where the correlation between the study variable and the ancillary variable is poor, reveal that the alternative estimator in Amahia et. al. (1989) is more efficient. Several other finite populations whose ρare neither too high as in population I nor too poor as in population II were considered and it was discovered that the competition for efficiency only rests with the two estimators suggested by Amahia et al (1989) and Rao (1966). These interesting comparative results are shown in Tables.
本文针对多特征调查中PPS抽样问题,比较了几种用于多特征PPSWR抽样的估计器的效率。从一个超总体模型中,我们计算了前两个有限总体的不同估计量的期望方差,以及每个估计量的确切偏差和方差。结果表明,Rao(1966)、Amahia et al.(1989)提出的估计量和Amahia et al.(1989)提出的替代估计量优于传统估计量。在种群I中,研究变量和辅助变量高度正相关,结果表明Amahia等人(1989)的估计器比替代估计器表现得更好。另一方面,从研究变量和辅助变量之间相关性较差的种群II中获得的结果表明,Amahia等人(1989)的替代估计器更有效。考虑了其他几个有限种群,它们的ρ既不像种群I中那样太高,也不像种群II中那样太低,并且发现效率的竞争仅取决于Amahia等人(1989)和Rao(1966)提出的两个估计。这些有趣的比较结果见表。