Based On The Auxiliary Information In Stratified Sampling Sensitivity Problem Analysis Of The Model

Sensitive questions are some problems relate to private confidential, such as: whether the drivers drunken driving, whether students cheated on exams, whether the taxpayer evaded tax and so on. The appearing of the randomized response technique (RRT) brings an easy and effective method to operate and implement survey, which effectively protects the confidentiality of the respondents as well as improves the probability of respondents’truly answers. Stratified sampling is a commonly used method in the sample survey which is simple and easy to operate. If layered properly, it can effectively improve the precision of parameter estimation. This paper first introduced some randomized response models of sensitive questions, and then discussed the application of these models in stratified sampling. It estimated the proportion of sensitive property characteristics π in stratified sampling including of Warner model, Simmons model and improved the expression of the parameter estimates.Because the sensitivity problems often involve the private confidential in the study of sensitive questions, the investigators usually gain little information from samples when the thinking of the popularity is not in place. While the information of existing historical data and experience before the start of the investigation becomes very important. Using of auxiliary information in study can effectively refine the sampling design to improve the accuracy of the estimated and save sampling costs. Therefore, this paper pulled in auxiliary variables in randomized device to estimate the unknown parameters respectively by Ratio estimation and regression estimation. Then the article discussed and compared estimator and the variance between the original Warner and Simmons models and Ratio and regression estimation models when the auxiliary information available. And then through the analysis of these random models, the survey finds that under certain conditions. The accuracy of the estimator can be improved by adding an auxiliary variable. Furthermore, through auxiliary information the survey can also obtain prior information and prior distribution, so the paper can use Bayesian statistical inference to estimate the parameters. This paper discussed the application of the Bayesian approach to sensitive issues. We can obtain the prior distribution by Priori information, using Bayesian estimation to find the a posteriori distribution and calculate the estimated amount. This can also reach to the purpose to use known auxiliary information effectively.