Chaudhuri and Mukerjee ORRT for two sensitive characteristics and their overlap

In this paper, we extend the optional randomized response technique (ORRT) developed by Chaudhuri and Mukerjee [Optionally randomized response techniques. Bull. Calcutta Statist. Assoc. 1985;34:225–230; Randomized response: theory and techniques. New York: Marcel Dekker, Inc.; 1988] to the situation of estimating the proportion of two sensitive characteristics and their overlap. Lee, Sedory and Singh [Estimating at least seven measures of qualitative variables from a single sample using randomized response technique. Stat Prob Lett. 2013;83(1):399–409; Estimation of odds ratio, attributable risk, relative risk, correlation coefficient and other parameters using randomized response techniques. Behaviormetrika. 2021;48:371–392.] have shown that their crossed model performs better than their simple model from an efficiency point of views. Here we investigated a further improvement in the crossed model along the lines of Chaudhuri and Mukerjee [Optionally randomized response techniques. Bull. Calcutta Statist. Assoc. 1985;34:225–230; Randomized response: theory and techniques. New York: Marcel Dekker, Inc.; 1988]. New unbiased estimators are proposed, their variance expressions are derived and estimators of variances are suggested. Lastly, we carry out a simulation study to investigate the behaviour of the proposed estimators with respect to their competitors.</p

Two-step calibration of design weights in survey sampling

<p>In this article, a new two-step calibration technique of design weights is proposed. In the first step, the calibration weights are set proportional to the design weights in a given sample. In the second step, the constants of proportionality are determined based on different objectives of the investigator such as bias reduction or minimum mean squared error. Many estimators available in the literature can be shown to be special cases of the proposed two-step calibrated estimator. A simulation study, based on a real data set, is also included at the end. A few technical issues are raised with respect to the use of the proposed calibration technique: both limitations and benefits are discussed.</p

Estimation of Finite Population Variance Using Scrambled Responses in the Presence of Auxiliary Information

<div><p>In this article, a new estimator for estimating the finite population variance of a sensitive variable based on scrambled responses collected using a randomization device is introduced. The estimator is then improved by using known auxiliary information. The estimators due to Das and Tripathi (1978: Sankhya) and Isaki (1983: JASA) are shown to be special cases of the proposed estimator. Numerical simulations are performed to study the magnitude of the gain in efficiency when using the estimator with auxiliary information with respect to the estimator based only on the scrambled responses. An idea to extend the present work from SRSWOR design to more complex design is also given.</p></div

Calibrated estimators in two-stage sampling

<p>We consider the problem of the estimation of the population mean of a study variable by assuming that the population means of an auxiliary variable are known at both stages of sample selection. The design weights at the first and second stages of sample selection are calibrated by optimizing the chi-squared type distance between the design weights and the new weights at both the first and second stages of sample selection. The regression type estimator in two-stage sampling is shown to be a special case. An application of the proposed estimators using a real data set is discussed.</p

Adjusted Kuk's model using two non sensitive characteristics unrelated to the sensitive characteristic

<p>In this paper, we adjust the Kuk (<a href="#cit0005" target="_blank">1990</a>) model for both protection and efficiency by making use of proportions of two non sensitive characteristics which are unrelated to the main sensitive characteristic of interest. Various situations, where the proportions of the two non sensitive characteristics in the population of interest are known and that when these proportions are unknown, have been investigated. We compared the adjusted model and Kuk's model through a simulation study from both the protection and efficiency points of view.</p