A two-step approach to ratio and regression estimation ofnite population mean using optional randomized response models (original) (raw)
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Scientia Iranica, 2019
In this study, we propose optional randomized response technique (RRT) models in binary response situation. The utility of proposed optional RRT models under stratification are also explored. Gupta et al.[1] introduced an ingenious idea of optional RRT model, where question may be sensitive for one respondent but may not be sensitive for another. This study focus on estimating π, the prevalence of sensitive attribute, ω, the sensitivity level of the underlying sensitive question when the proportion of unrelated innocuous attribute π x is unknown. A new multi-question approach is proposed for estimation of parameters (π, ω). A comparison between proposed optional RRT models and corresponding full RRT models are carried out numerically under simple and stratified random sampling.
Communications in Statistics - Simulation and Computation, 2018
In this study, we propose optional randomized response technique (RRT) models in binary response situation. Gupta, Gupta, and Singh (2002) introduced the basic premise of optional RRT model, that a question may be sensitive for one respondent but may not be sensitive for another. In an optional RRT model, a respondent is requested to provide a scrambled response only if he/she considers the question is sensitive. Otherwise, the respondent provides a truthful response. This study focus on estimating p, the prevalence sensitive characteristics, and x, the sensitivity level of the underlying sensitive question. Two-question and split-sample approaches are used for parameters ðp; xÞ estimation. A comparison between proposed optional RRT models and corresponding full RRT models are carried out numerically.
Communications in Statistics - Simulation and Computation, 2018
Motivated by some recent improvements for mean estimation in finite sampling theory, we propose, in a design-based approach, a new class of ratio-type estimators. The class is initially discussed on the assumption that the study variable has a nonsensitive nature, meaning that it deals with topics that do not generate embarrassment when respondents are directly questioned about them. Under this standard setting, some estimators belonging to the class are shown and the bias, mean square error and minimum mean square error are determined up to the first-order of approximation. The class is subsequently extended to the case where the study variable refers to sensitive issues which produce measurement errors due to nonresponses and/or untruthful reporting. These errors may be reduced by enhancing respondent cooperation through scrambled response methods that mask the true value of the sensitive variable. Hence, four methods (say the additive, multiplicative, mixed and combined additive-multiplicative methods) are discussed for the purposes of the article. Finally, a simulation study is carried out to assess the performance of the proposed class by comparing a number of competing estimators, both in the sensitive and the nonsensitive setting.
Bayesian analysis of optional unrelated question randomized response models
Communications in Statistics, 2020
The randomized response technique (RRT) is an effective method designed to obtain the sensitive information from respondents while assuring the privacy. Narjis and Shabbir [Narjis, G., and J. Shabbir. 2018. Estimation of population proportion and sensitivity level using optional unrelated question randomized response techniques. Communications in Statistics-Simulation and Computation 0 (0):1-15] proposed three binary optional unrelated question RRT models for estimating the proportion of population that possess a sensitive characteristic ðpÞ and the sensitivity level ðxÞ of the question. In this study, we have developed the Bayes estimators of two parameters ðp, xÞ for optional unrelated question RRT model along with their corresponding minimal Bayes posterior expected losses (BPEL) under squared error loss function (SELF) using beta prior. Relative losses, mean squared error (MSE) and absolute bias are also examined to compare the performances of the Bayes estimates with those of the classical estimates obtained by Narjis and Shabbir (2018). A real survey data are provided for practical utilizations.
Improved estimation of mean in randomized response models
Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics
The present investigation considers the problem of estimating the mean of a sensitive quantitative variable µA in a human population survey, using the scrambled response technique suggested by Ryu, Kim, Heo and Park (On stratified randomized response sampling, Model Assisted Statistics and Application 1(1), 31-36, 2005-2006). Specifically, using the prior estimate (or guessed mean) of the mean of a population, a family of estimatorsμ Ak is presented to estimate the population mean µA, and its properties are examined. The optimum value of the degree k(0 ≤ k ≤ 1) of the belief in the prior estimate depends, besides others, on the unknown population parameters, e.g. mean and variance, so the proposed family of estimators may have limited practical applications. In an attempt to overcome this problem, another estimator based on the estimated optimum value of k has been proposed. The proposed estimator has been compared with the Ryu et al. and Hussain and Shabbir (Improved estimation procedure for the mean of a sensitive variable using randomized response model, Pakistan Journal of Statistics 25(2), 205-220, 2009) estimators assuming simple random sampling with replacement.
Scrambling Reports: New Estimators for Estimating the Population Mean of Sensitive Variables
Mathematics, 2023
Warner proposed a methodology called randomized response techniques, which, through the random scrambling of sensitive variables, allows the non-response rate to be reduced and the response bias to be diminished. In this document, we present a randomized response technique using simple random sampling. The scrambling of the sensitive variable is performed through the selection of a report Ri, i = 1, 2, 3. In order to evaluate the accuracy and efficiency of the proposed estimators, a simulation was carried out with two databases, where the sensitive variables are the destruction of poppy crops in Guerrero, Mexico, and the age at first sexual intercourse. The results show that more accurate estimates are obtained with the proposed model.
A New Improved Estimator of Population Mean in Partial Additive Randomized Response Models
Hacettepe Journal of Mathematics and Statistics, 2017
In this study, we have developed a new improved estimator for the population mean estimation of the sensitive study variable in Partial Additive Randomized Response Models (RRMs) using two non-sensitive auxiliary variables. The mean squared error of the proposed estimator is derived and compared with other existing estimators based on the auxiliary variable. The proposed estimator is compared with [19],[5] and [13] estimators in performing a simulation study and is found to be more efficient than other existing estimators using non-sensitive auxiliary variable. The results of the simulation study are discussed in the final section.
Estimating functions in survey sampling using randomized response trials
Model Assisted Statistics and Applications, 2015
In sample surveys it is often difficult to obtain true responses to questions of a personal or sensitive nature, such as questions regarding savings, drug use, or extramarital affairs. To avoid providing the requisite information, or to avoid embarrassment, some respondents may refuse to give answers or may give false answers. Thus the estimates obtained from a direct survey on such topics would be biased and inferences drawn from these would be erroneous. In order to solve this problem a number of randomized response techniques (RRT), pioneered by Warner [14], have been developed. Summaries of such techniques have been made by Chaudhuri and Mukherjee [4], Mukhopadhyay [11], and Chaudhuri [3]. Here we shall find an optimal estimator of the population total of a sensitive character y in surveys using randomized response techniques by an application of optimal estimating functions.
Estimation of sensitive quantitative characteristics in randomized response sampling
This paper considers the problem of procuring honest responses for sensitive quantitative characteristics. An alternative survey technique is proposed, which enables us to estimate the population mean unbiasedly and to gauge how sensitive a survey topic is. An asymptotically unbiased estimator of sensitivity level is proposed, and conditions for which unbiased estimation for population variance being available is also studied. In addition, an efficiency comparison is worked out to examine the performance of the proposed procedure. It is found that higher estimation efficiency results from higher variation of randomization device.
Journal of Statistical Theory and Practice, 2022
There are situations in survey sampling where the study characters are sensitive. Due to the sensitivity of characters, practitioners don't get the actual response. Randomized response technique (RRT) models are developed to reduce the bias raised by an evasive response on the sensitive variable. The measurement error (ME) is usually always present in the surveys so we need to study the RRT models with ME. We propose an estimator to predict the population mean of a sensitive variable in the influence of ME. The properties of the proposed estimator are studied and comparisons are made with the existing estimators. At last, a simulation study is executed to illustrate the results numerically.