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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.

When researchers conduct surveys seeking sensitive, socially stigmatized information, respondents, on average, modify their answers to represent themselves favorably. To overcome this issue, researchers may use Randomized Response Technique (RRT) models. Recently, Parker et al. proposed a model that incorporates some of the most critical recent quantitative RRT advancements—mixture, optionality, and enhanced trust—into a single model, which they called a Mixture Optional Enhanced (MOET) model. We now improve upon the MOET model by incorporating auxiliary information into the analysis. Positively correlated auxiliary information can improve the mean response estimation through use of a ratio estimator. In this study, we propose just such an estimator for the MOET model. Further, we investigate the conditions under which the ratio estimator outperforms the basic MOET estimator proposed by Parker et al. in 2024. We also consider the possibility that the collection of auxiliary information may compromise privacy; and we study the impact of privacy reduction on the overall model performance as assessed by the unified measure (UM) proposed by Gupta et al. in 2018.

The calibration method is used in stratified random sampling in the presence of measurement error to achieve optimum strata weights for better precision. In this study we attempt to analyze the behaviour of calibration estimators with different types of distance measures in the presence of measurement error for the estimation of population mean under stratified random sampling. The proposed estimators are compared with the estimators in the absence of measurement error. A simulation study has been carried out to evaluate the proposed estimators.

This study examines the effect of measurement error on binary Randomized Response Technique models. We discuss a method for estimating and accounting for measurement error and untruthfulness in two basic models and one comprehensive model. Both theoretical and empirical results show that not accounting for measurement error leads to inaccurate estimates. We introduce estimators that account for the effect of measurement error. Furthermore, we introduce a new measure of model privacy using an odds ratio statistic, which offers better interpretability than traditional methods.

The Quantitative Randomized Response Technique (RRT) can be used by researchers to obtain honest answers to questions that, due to their sensitive (socially undesirable, dangerous, or even illegal) nature, might otherwise invoke partially or completely falsified responses. Over the years, Quantitative RRT models, sometimes called Scrambling models, have been developed to incorporate such advancements as mixture, optionality and enhanced trust, each of which has important benefits. However, no single model incorporates all of these features. In this study, we propose just such a unified model, which we call the Mixture Optional Enhanced Trust (MOET) model. After developing methodologies to assess MOET based on standard approaches and using them to explore the key characteristics of the new model, we show that MOET has superior efficiency compared to the Quantitative Optional Enhanced Trust (OET) model. We also show that use of the model’s mixture capability allows practitioners to optimally balance the model’s efficiency with its privacy, making the model adaptable to a wide variety of research scenarios.

In this paper, a general class of estimators is proposed for estimating the finite population mean for sensitive variable, in the presence of measurement error and non-response in simple random sampling. Expressions for bias and mean square error up to first order of approximation, are derived. Impact of measurement errors is examined using real data sets, including the survey conducted at Quaid-i-Azam University, Islamabad. Simulated data sets are also used to observe the performance of the proposed estimators in comparison to some other estimators. We obtain the empirical bias and MSE values for the proposed and the competing estimators.

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.

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.

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.

Auxiliary information is frequently used to improve the accuracy of the estimators when estimating the unknown population parameters. In this paper, we propose a new difference-cum-exponential type estimator for the finite population mean using auxiliary information in simple random sampling. The expressions for the bias and mean squared error of the proposed estimator are obtained under first order of approximation. It is shown theoretically, that the proposed estimator is always more efficient than the sample mean, ratio, product, regression and several other existing estimators considered here. An empirical study using 10 data sets is also conducted to validate the theoretical findings.

This paper proposes an optional RRT method to estimate the sensitivity level of personal interview survey questions with quantitative response. The method is similar to the one used by Gupta et al. (2002) but estimates both the average response level and the sensitivity level of the question. A numerical example explains the estimation process and a simulation study assesses the effectiveness of the proposed method. We also compare the performance of the proposed estimator with the “Full” and “Partial” randomized response models.

Recently a new generalized estimator for population variance using information on the auxiliary variable has been introduced by Asghar et al. (2014). In that paper there was some inaccuracy in the bias and MSE expressions. In this paper, we provide the correct expressions for bias and MSE of the Asghar et al. (2014) estimator, up to the first order of approximation. We also propose a new generalized exponential type estimator for population variance which performs better than the existing estimators. Four data sets are used for numerical comparison of efficiencies.