【作者】 刘升学；

【导师】 高歌；

【作者基本信息】 苏州大学 ， 流行病与卫生统计学， 2008， 硕士

【摘要】 目的:为了调查总体在不同时间上的水平及其变化、累计或平均水平,须采用连续调查,我国建立的统计调查体系是以经常性的连续调查为主体。对固定样本进行多次调查存在代表性下降和样本疲劳两个严重问题;在不同次调查中重新抽取不同的新样本,也存在另几个严重问题:如不能很好反应总体在不同时间的变化,不能利用固定样本的前期资料对现期总体作出精度较高的回归组合估计,与固定样本相比,调查费用、时间、难度更高等等。为了权衡这两方面的问题,国内外的统计学家早已研究出样本轮换(在样本容量不变的前提下,每隔一定时间更换部分样本单位)的好方法。样本轮换(Sample rotation)由于既保留了部分原有单位,又增加了部分新样本单位,所以兼有全新样本与固定样本的优点,能在抽样费用与抽样精度之间取得平衡,是减少和控制非抽样误差的重要手段。抽样调查的关键是抽样设计。国内外对一次性(横断面)调查的抽样设计研究较多,理论及方法比较成熟;而对于连续调查的抽样设计,主要局限于对简单随机抽样调查中的样本轮换问题的研究,复杂抽样方法下连续调查中样本轮换问题的研究甚少,鉴于此,本文在分层简单随机随机抽样、整群抽样、分层整群抽样、两阶段抽样、分层两阶段整群抽样的复杂抽样方法下,对连续调查中的样本轮换相应统计量的计算公式,进行推导证明,填补相应空白,并探讨以上各复杂抽样方法下连续调查中样本轮换问题的实际应用。方法:在调查方法的设计及公式的推导中,分层抽样的理论、整群抽样的理论、二阶段抽样的理论、回归估计量的理论、比率估计量的理论、连续调查的理论、样本轮换的理论及概率统计的基本理论被应用;在调查方法及统计公式的实际应用中,采用了分层简单随机抽样、整群抽样、分层整群抽样、两阶段抽样,分层两阶段整群抽样的抽样调查方法,及医学体检、现场问卷调查的研究方法。结果:分别在分层简单随机抽样、整群抽样、分层整群抽样、两阶段抽样、分层两阶段整群抽样五种复杂的抽样调查方法下,对连续调查中的样本轮换,推导出了总体组合估计量、总体组合估计量的方差、总体组合估计量方差的估计量、最优样本轮换率、最优组合估计权数的计算公式。同时于2005-2007年对广东大亚湾核电运营公司(DNMC)职工的体质指数(BMI)连续进行三次抽样调查,于2006-2007年对苏州大学新校区在校学生考试作弊次数连续进行两次抽样调查,采用本项目研究的五种复杂抽样调查方法下连续调查中样本轮换的相应统计量计算公式进行参数估计,并对其进行了抽样精度比较。连续调查中采用样本轮换的抽样方法与固定样本的抽样方法相比,抽样精度,分层简单随机抽样提高29.5倍,整群抽样提高5倍,分层整群抽样提高3.2倍,两阶段抽样提高24倍,分层两阶段整群抽样提高18倍。可见,连续调查中采用样本轮换的抽样方法与固定样本的抽样方法相比,抽样精度提高数倍甚至数十倍,所推导证明的公式取得了良好的实际应用效果。结论:本研究所推导证明的五种复杂抽样调查方法下连续调查中的样本轮换的各相应统计量计算公式,方法科学可行、参数估计精度高,具有创新性和较大的理论与实际意义。更多还原

【Abstract】 Objective: For the survey of population’s value, variation, accumulative total and the average, we need successive survey, which is the main body of our country’s survey system. To use the fixed sample time after time, there are two serious problems of that one is the reduction of sample representation, another one is sample fatigue. However, using completely new sample in each survey also has several problems. Firstly, it couldn’t reflect the change of population in continuous time. Secondly, we couldn’t employ the combined regression estimation without the prior period data of fixed sample by which the estimate precision is better than that of common one. Thirdly, comparing with fixed sample, completely new sample need more cost and time. To balance these two aspects, statisticians have excogitated the good method of sample rotation (under the same sample size, we replace part of the sample units each survey). For sample rotation, it retains some of the original units and add some new sample units, so it assembled the advantages of both the fixed sample and completely new sample, striking the balance between sampling cost and sampling precision. It was the means to reduce and control non-sampling error, unifying the sampling efficiency and sampling precision.The key of sampling survey is sampling design. Sampling design for single survey (transect survey) is widely researched at home and abroad, of which theories and methods are relatively mature. However, for sampling design of successive survey, the research for sample rotation is mainly confined to the simple random sample survey. It is very few that the research for sample rotation of successive survey under complicated sampling methods. So, in this paper, we deduced the formulae for relevant statistic under stratified simple random sampling, cluster sampling, stratified cluster sampling, two-stage sampling and stratified two-stage cluster sampling for sample rotation of successive survey, filled the corresponding gap. Moreover, the practical application was explored.Methods: The theories of stratified sampling, cluster sampling, two-stage sampling, regression estimate, ratio estimate, successive survey, sample rotation and probability statistic were employed for the design and formula deduction. During the practical application of sampling methods and the deduced formulae, we employed the survey methods of stratified simple random sampling, cluster sampling, two-stage sampling, stratified cluster sampling, stratified two-stage cluster sampling, and also the methods of medical physical examination and questionnaire survey.Results: For the sample rotation of successive survey, under the five complicated sampling methods of stratified simple random sampling, cluster sampling, two-stage sampling, stratified cluster sampling, stratified two-stage cluster sampling, we deduced the formulae for combined estimate of population mean as well as its variance, for the estimate of variance, for the optimum sample rotation rate and for the optimum weight. Meanwhile, we conducted two sampling surveys. One is the sampling survey of staff’s body mass index (BMI) of Daya Bay Nuclear Power Operation and Management Co.,Ltd (DNMC) in Guangdong in the years 2005-2007 for three times consecutively. The other one is the sampling survey of students’cheating frequency in examination in new campus of Soochow University in the years 2006-2007 for two times consecutively. Then these deduced and proved formulae were applied to the parameter estimation, moreover, the sampling precision was detected. As to the sampling precision, the method of sample rotation comparing with that of fixed sample for successive survey, it was 29.5 times higher for stratified simple random sampling, 5 times higher for cluster sampling, 3.2 times higher for stratified cluster sampling, 24 times higher for two-stage sampling and 18 times higher for stratified two-stage cluster sampling. That was to say, the sampling precision were several times higher or even tens times higher for sample rotation than for fixed sample. The application result of these deduced and proved formulae was very good. Conclusion: During this study, for the sample rotation of successive survey under the five complicated survey methods, the corresponding formulae deduced and proved for calculating statistic are scientific, by which the estimated precision is highly increased. This study is originality innovation and significant of theory and reality.更多还原