Bayesian Estimation Under Of Randomized Response Model

In socioeconomic investigation we sometimes need facts about highly personalmattres. For example, drug taking, gambling, history of induced abortion, homosexuality,tax evasion etc. The inquirer often feels a delicacy and uncomfortable in asking directquestionsabout private and confidential subjects. Also, people would refuse to answer orlie to such sensitive issues. In order to reduce rates of nonresponse and biased response, aintelligent response device was introduced by Warner (1965) and popularized by severalother researchers who followed his lead.Later, Simmons, Mangat etc., put forward themethod of randomized survey unrelated question, but the discussion of the unknownparameters is a classical methods and in addition to the classical approach, there is a kindof important method in mathematical statistics the Bayesian method. Although the past40years many randomized response models was presented, but the Bayesian estimationis seldom to be used in this field. Our main work is to import Bayesian estimation, whichare used to randomized response models about the qualitative sensitive problem.Bayesian estimation of population proportion of a sensitive characteristic is proposed byadopting a simple beta distribution and a mixture of Beta distributions as quantificationof prior information using simple random sampling with replacement. To study theperformance of Bayesian estimat-ors we have used Mean Squared Error (MSE) and/or Relative Efficiency (RE) asperformance criterion.ChapterⅠ, the background knowledge and main work of the sampling survey, thesampling methods of sensitive problem and Bayesian estimation were given.ChapterⅡ, the summary of classical sampling design, for instance, WarnerRandomized Response Technique, Simmons model, Mangat(1990) RandomizedResponse model, Mangat(1994) Randomized Response model, simple random sampling,stratified and so on, And introduce the relevant theoretical knowledge of Bayesianestimation.ChapterⅢ, In the primary randomization device Mangat(1994) introduces theBayesian estimation, respectively to calculate the simple prior and simple random sampling, mixture prior and simple random sampling, simple prior and the stratifiedrandom sampling Bayesian estimation, and compare the maximum likelihood estimation.ChapterⅣ, In the secondary randomization device Mangat(1994) introduces theBayesian estimation, respectively to calculate the simple prior and simple randomsampling, mixture prior and simple random sampling, simple prior and the stratifiedrandom sampli-ng Bayesian estimation, and compare the maximum likelihood estimation.ChapterⅤ, Given attributes randomization strategy the general theory of Bayesianestimation.ChapterⅥ,Summarizing what I have done and what should be done.