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In this paper, Randomized Response technique (RRT) is used to propose some separate and combined variance estimators for a sensitive variable using stratified random sampling. The performances of the proposed estimators are examined using a unifed measure of respondent privacy and estimator efficiency.

In social surveys involving questions that are sensitive or personal in nature, respondents may not provide correct answers to certain questions asked by the interviewer. The impact of this nonresponse or inaccurate response becomes even more acute in the case of small area estimation (SAE) where we already have the problem of small sample size coming from the small area. To obtain a truthful response, we use randomized response techniques in each small area. We assume that a non-sensitive auxiliary variable, highly correlated with the study variable, is available. We use the word model in two senses — one in the context of population models, i.e. the relationship between the study variable and the auxiliary variable; and second, the scrambled response model. We focus on the problem of estimating small area total and examine its performance both theoretically and numerically.

Variance estimation is a well-studied topic in survey sampling but not much work has been done in this area in the context of Randomized Response Technique (RRT) models. We propose here some variance estimators for sensitive variables using auxiliary information. We examine the performance of the proposed estimators through a simulation study and through a numerical example.

The article presents predictive estimation of population mean of the study variable in Ranked Set Sampling (RSS). It is shown that the predictive estimators in RSS using mean per unit estimator, ratio estimator and regression estimator as predictor for non-sampled values are equivalent to the corresponding classical estimators in RSS. On the other hand, when product estimator is used as predictor, the resulting estimator differs from the classical product estimator under RSS. Expressions for the Bias and the Mean Squared Error (MSE) of the proposed estimators are obtained up to first order of approximation. A simulation study is conducted to observe the performance of estimators under predictive approach.

Systematic sampling has been facing two problems since its beginning; situational complications, e.g., population size N not being a multiple of the sample size n, and unavailability of unbiased estimators of population variance for all possible combinations of N and n. These problems demand a sampling design that may solve the said problems in a practicable way. In this paper, therefore, a new sampling design is introduced and named as, “Modified Systematic Sampling with Multiple Random Starts”. Linear systematic sampling and simple random sampling are the two extreme cases of the proposed design. The proposed design is analyzed in detail and various expressions have been derived. It is found that the expressions for linear systematic sampling and simple random sampling may be extracted from these expressions. Finally, a detailed efficiency comparison is also carried out in this paper.