Some Contributions To Scrambled Randomized Response Technique Using Auxiliary Variable For Parameters In Finite Population

Abstract

In this dissertation, some generalized scrambled randomized response models for sensitive characteristics have been proposed using two scrambling variables. Similarly, some regression, ratio, exponential, regression-cum-exponential, regression-cum-ratio and ratio in exponential estimators have been proposed to estimate population characteristics for sensitive surveys using auxiliary information. The estimators are proposed for simple random sampling design for both single-phase sampling and two-phase sampling. In Chapter 1, the discussion on sensitive surveys has been made. The techniques to collect information on sensitive characteristics such as randomized response and scrambled randomized response techniques have been introduced into more detail. Further, the use of auxiliary information and two-phase sampling have been illustrated. In Chapter 2, the review of literature regarding the use of auxiliary information in single-phase sampling and two-phase sampling have been discussed with the estimators developed by different statisticians for both sensitive and non-sensitive surveys. Various development on randomized response models in literature have also been presented. The major work of this dissertation start from Chapter 3. In this chapter, four generalized scrambled randomized response models have been proposed combining additive and multiplicative models. These four generalized models have been proposed using two scrambling variables with known distribution. The expressions of the mean, variance, covariance and correlation have been derived for each of the proposed models. Additionally, the privacy measure have been derived for some existing models presented in literature review and the proposed models. The privacy protection comparisons between existing models and proposed models have also been discussed. In Chapter 4, the generalized exponential-type estimators have been constructed using two auxiliary variables to estimate population mean of the sensitive variable. The bias and mean square error have been derived for each proposed estimator. To examine the performance of the proposed generalized estimators, the simulation study have been performed under the observed response using additive and proposed scrambled randomized response models. In Chapter 5, the regression, ratio, regression-cum-ratio, regression-cum exponential and ratio in exponential-type estimators have been proposed under two-phase sampling to estimator population mean of sensitive study variable. The estimators have been proposed for three cases of two-phase sampling such as full-information-case, partial-information-case and no-information-case. The x expressions of the bias and mean square error have been derived for each proposed estimator. Additionally, the simulation study has been conducted to examine the performance of estimator using additive and proposed models. To estimate the population variance of sensitive study variable, some exponential estimators have been proposed in Chapter 6. These estimators have been presented for both single-phase and two-phase sampling. In this chapter, the additive model is considered to estimate population variance. The expressions of the bias and mean square error have been derived. The simulation study have also been presented for both single-phase and two phase sampling.