Improvements Of The Collocated Sampling And Randomized Response Survey With Additional Information

In socioeconomic investigations we sometimes need facts about highly personal mat-ters. For example, drug taking, gambling, history of induced abortion, homosexuality, taxevasion etc. The inquirer often feels a delicacy and uncomfortable in asking direct ques-tions about private and confidential subjects. Also, people would refuse to answer or lie tosuch sensitive issues. In order to reduce rates of nonresponse and biased response, a intel-ligent response device was intruduced by Warner(1965) and popularized by several otherresearchers who followed his lead. Considering the peculiarity of sensitive problems, forinstance, the hospital should have some records about abortions of women, the governmentshould have some tax evasion records. This records can be efective and reasonably utilized.Until now, few scholars have discussed how to estimate the parameters of the populationwhen we know sensitive information about some individuals which called additional infor-mation in this article. Our main work is to improve estimators when additional informationabout the population is available.Furthermore, the unequal probability sampling design using auxiliary variables gen-erally has a high efciency. For example, πPS sample design is the unequal probabilitysampling design without replacement whose inclusion probability is proportional to its size.This kind of design is more emphasized than other designs in the real application as its sam-ple is without repetition units. Since a long time ago, how to construct and implement πPSsample design is a open problem. A good πPS sampling design is not only a design withfixed sample size and reserved inclusion probability, but also a design with high precisionand quickly sampling. Ha′jek(1981) introduced a πPS sampling design with fixed samplesize, but unfortunately it is rather time-consuming to get a suitable sample and its inclusionprobability is roughly equal to the reserved one. Joyce(1972) proposed a strict πPS sam-pling design with a random sample size which called collocated sampling. The collocatedsampling has advantage over Poisson sampling in the variance of sample size and a slightadvantage in estimation accuracy. The powerful idea of Conditional Poisson Sampling in-spired us. We suggest a new design that keep sampling using collocated sampling until the sample size is exactly n which called Conditional Collocated Sampling. For one hand, wediscuss the formal expressions of inclusion probabilities, another hand, in order to show thereal worth of the new design in practical and its advantage in estimation, we simulate eightdiferent super-population models to compare the proposed design with Conditional PoissonSampling.Chapter I, the background knowledge and related definitions of the sampling survey,the sampling methods of sensitive problems and the unequal probability sampling designwere introduced. To be better understand this article, some basic concepts, theories and thecorresponding mathematical symbols were given.Chapter II, the summary of classical sampling design, for instance, warner randomizedresponse technology, Eichhorn scrambled response, Conditional Poisson sampling, Collo-cated sampling,2PπPS sampling design etc.Chapter III, a general method-based additional information to increase the efciencyof estimation under randomized response surveys is proposed for the first time. we havetheorized about the estimation of population proportion with qualitative sensitive problem.A example of the suggested estimators is given.Chapter IV, we have theorized about the estimation of population mean with quanti-tative sensitive problem. The comparison of the suggested estimators is theoretically andnumerically made with classical estimators.Chapter V, we suggest a new design which called Conditional Collocated Sampling.For one hand, we discuss the formal expressions of inclusion probabilities, another hand, inorder to show the real worth of the new design in practical and its advantage in estimation,we simulate eight diferent super-population models to compare the proposed design withConditional Poisson sampling.Chapter VI, summarying what I have done and what shoud be done.