Pseudo-Bayes and pseudo-empirical Bayes estimators in randomized response sampling

In this article, new pseudo-Bayes and pseudo-empirical Bayes estimators for estimating the proportion of a potentially sensitive attribute in a survey sampling have been introduced. The proposed estimators are compared with the recent estimator proposed by Odumade and Singh [Efficient use of two decks of cards in randomized response sampling, Comm. Statist. Theory Methods 38 (2009), pp. 439–446] and Warner [Randomized response: A survey technique for eliminating evasive answer bias, J. Amer. Statist. Assoc. 60 (1965), pp. 63–69].     

Randomized Response Techniques Using Maximum Likelihood Estimator

The randomized response (RR) technique with two decks of cards proposed by Odumade and Singh (2009) can always be made more efficient than the RR techniques proposed by Warner (1965), Mangat and Singh (1990), and Mangat (1994) by adjusting the proportion of cards in the decks. Arnab et al. (2012) generalized Odumade and Singh strategy (2009) for complex survey designs and wider class of estimators. In this paper improvement of Arnab et al. (2012) estimator has been made by using maximum likelihood method.     

A modified two-stage randomized response model for estimating the proportion of stigmatized attribute

The survey related to stigmatized characteristics leads to the non-response problem if it is conducted according to classical (direct) methods, especially, developed for non-sensitive issues; therefore, it needs to be applied appropriate survey methodology to get a reliable response from respondents in incriminating issues. Randomized response model is one of the most recent methods which is attracting the attention of survey practitioners to deal with the problems of non-response because it protects the privacy of individuals in order to acquire the truthful response. The present work proposes a new two-stage randomized response model to get rid of misleading response or non-response due to the stigmatized nature of attribute under the study. The proposed randomized response model results in the unbiased estimator of population proportion possessing the sensitive attribute. The properties of the resultant estimator have been studied and empirical comparisons are performed to show its dominance over existing estimators. Suitable recommendations have been put forward to the survey practitioners.     

Improved estimation methods for unrelated question randomized response techniques

The randomized response technique (RRT) is an important tool, commonly used to avoid biased answers in survey on sensitive issues by preserving the respondents’ privacy. In this paper, we introduce a data collection method for survey on sensitive issues combining both the unrelated-question RRT and the direct question design. The direct questioning method is utilized to obtain responses to a non sensitive question that is related to the innocuous question from the unrelated-question RRT. These responses serve as additional information that can be used to improve the estimation of the prevalence of the sensitive behavior. Furthermore, we propose two new methods for the estimation of the proportion of respondents possessing the sensitive attribute under a missing data setup. More specifically, we develop the weighted estimator and the weighted conditional likelihood estimator. The performances of our estimators are studied numerically and compared with that of an existing one. Both proposed estimators are more efficient than the Greenberg's estimator. We illustrate our methods using real data from a survey study on illegal use of cable TV service in Taiwan.     

数量特征敏感问题问卷设计

目前,数量特征敏感问题调查主要采用随机化策略,该策略需使用随机化装置,从而需要在现场实施。提出一种问卷设计技术,该技术用无关问题替代随机化装置,因而不需要调查者亲临现场,不受调查规模及调查单位聚散的限制,使得调查更加方便、实用、经济。给出了相应的无偏估计量,推算出估计量的方差和方差的估计量并举例说明。     

Generalized franklin's model for randomized response sampling

In this paper we introduce two estimators of a population proportion when randomized response sampling with a normal randomizing distribution is used* The estimators have been obtained by using the method of moments. Both of the proposed estimators are shown to be more efficient than the corresponding estimators of Eranklin (1989 b).     

基于随机化回答模型的最低工资敏感性问题研究

针对最低工资调查中出现的敏感性问题,引入随机化回答技术,并针对定性和定量两类敏感性问题,分别引入不同的随机化回答模型。同时还考虑到最低工资调查中,不同调查单位对同一问题敏感程度不相同的特性,在定量问题的随机化回答模型中引入敏感性水平,对原有模型进行有效的改进,使被调查者能够更加积极配合最低工资调查,从而能够进一步减少由于各类敏感性问题造成的非抽样误差。这套随机化处理方法还可推广应用到其他类型的敏感性问题中。     

A note on the randomized response technique

It is pointed out that the usual estimators for the parameters of a randomized response model are not, contrary to popular belief, maximum likelihood estimators.     

Maximum likelihood estimation of sensitive proportion using repeated randomized response techniques

Randomized response techniques are designed to obtain usable data on sensitive issues while protecting the privacy of individuals. In this paper, based on repeating the randomized response technique, a new technique called repeated randomized response is introduced to increase the protection of privacy and efficiency of estimator for proportion of sensitive attribute. By using this technique, the proportion of academic cheating is estimated among students of Shahid Chamran University of Ahvaz, Ahvaz, Iran.     

A new two sample type-II progressive censoring scheme

In this paper we introduce a new type-II progressive censoring scheme for two samples. It is observed that the proposed censoring scheme is analytically more tractable than the existing joint progressive type-II censoring scheme proposed by Rasouli and Balakrishnan. The maximum likelihood estimators of the unknown parameters are obtained and their exact distributions are derived. Based on the exact distributions of the maximum likelihood estimators exact confidence intervals are also constructed. For comparison purposes we have used bootstrap confidence intervals also. One data analysis has been performed for illustrative purposes. Finally we propose some open problems.     

N the theory of randomized responses to two sensitive questions

This paper sets forth a stochastic model which can be applied to randomized response designs wherein more than one question is sensitive of stigmatizing. Using three specific designs applied to a pair of stigmatizing or sensitive traits leading to two by two contingency tables, it is proved that if the two traits are statistically independent then the responses are also and conversely. The converse statement gives the support we need for inference to be made on the traits based on the randomized responses.     

Variance estimation with randomized response

Presenting a general procedure of eliciting a randomized response (RR) from selected persons in order to estimate the total of a sensitive variable related to a finite survey population, we consider two estimators along with variance estimators treating the case of sampling with probabilities proportional to (known) size measures (PPS) with replacement (WR), drawing analogies with multi-stage sampling and note their relative efficacies.     

Statistical inference for two exponential populations under joint progressive type-I censored scheme

In this article, we introduce a new scheme called joint progressive type-I (JPC-I) censored and as a special case, joint type-I censored scheme. Bayesian and non Bayesian estimators have been obtained for two exponential populations under both JPC-I censored scheme and joint type-I censored. The maximum likelihood estimators of the parameters, the asymptotic variance covariance matrix, have been obtained. Bayes estimators have been developed under squared error loss function using independent gamma prior distributions. Moreover, approximate confidence region based on the asymptotic normality of the maximum likelihood estimators and credible confidence region from a Bayesian viewpoint are also discussed and compared with two Bootstrap confidence regions. A numerical illustration for these new results is given.     

A Two-stage Binary Optional Randomized Response Model

Social desirability bias (SDB) is the tendency in respondents to answer questions untruthfully in the hope of giving good impression to others. SDB occurs when the survey question is highly sensitive or personal. The Randomized Response Technique (RRT) is one of several methods to get around SDB in face-to-face interview surveys involving sensitive questions. In this article, we first review some of the existing binary response RRT models. Then, we propose a new model—Two-Stage Binary Optional RRT model. Much of the focus is on estimating π, the prevalence of sensitive characteristic, and ω, the sensitivity level of the underlying question. We discuss the asymptotic properties of our estimators and present some simulation results. It turns out that the proposed Two-Stage Binary Optional RRT model is more effective than the Optional RRT model proposed by Gupta (2001).     

Estimation of the Mean and Standard Deviation of the Logistic Distribution Based on Multiply Type-II Censored Samples

In this paper, we discuss the problem of estimating the mean and standard deviation of a logistic population based on multiply Type-II censored samples. First, we discuss the best linear unbiased estimation and the maximum likelihood estimation methods. Next, by appropriately approximating the likelihood equations we derive approximate maximum likelihood estimators for the two parameters and show that these estimators are quite useful as they do not need the construction of any special tables (as required for the best linear unbiased estimators) and are explicit estimators (unlike the maximum likelihood estimators which need to be determined by numerical methods). We show that these estimators are also quite efficient, and derive the asymptotic variances and covariance of the estimators. Finally, we present an example to illustrate the methods of estimation discussed in this paper.     

A stratified randomized response model for sensitive characteristics using non identical trials

Abstract

Stratification provides a powerful tool for improving the efficiency and, being suitable for various sampling situations, it is commonly used in practice. Motivated by the utility of stratified sampling scheme, we focus on studying behavior of the estimator of proportion of a sensitive attribute while dealing with non-identical Bernoulli trials in survey research. The objective is achieved by considering a general randomized response model. Relative efficiency comparisons are presented along with cost analysis by considering different cost functions. Stratified random sampling is observed to be yielding more precise estimators.     

Generalizations of a contamination model for continuous type random variables

In 1965, Stanley Warner (Warner, 1965) introduced a model for contaminating discrete type random variables. He presented this scheme as being potentially useful in survevs where sensitive in-formation is being gathered. Since that time much research has been conducted and many papers written on the development of these discrete type randomized response models. More recently, atten-tion has been focused on the application of randomized response type models for preservation of confidentiality in existing data files (Boruch 1971 and 1972, Ranney 1975, Felligi 1974, and Inge-marsson 1975). In 1974, Poole (Poole, 1974) introduced a randomized response model for a positive continuous type random variable which was basically a continuous variable analog of the discrete variable Warner model. In this paper the results of the 1974 paper are extended to a lt-dimensional continuous type random variable in k-dimensional Euclidean space.     

Estimating a distribution for each category of a sensitive variate

The use of a Randomized Response (RR) design makes it possible to estimate the distribution of a sensitive variate. In this paper, the estimation of the distribution of a non-sensitive variate for each category of a sensitive variate is considered for the case where data on the sensitive variate is obtained by use of an RR procedure. Simple estimators are developed without making any distributional assumptions about the non-sensitive variate. However, if distributional assumptions are made, it is shown that the EM algorithm may be used to compute Maximum Likelihood estimates. Computational comparisons of the estimators, using simulation, indicate that the simple estimators perform well, particularly for large sample sizes.     

Bias of maximum likelihood estimators of the response standard deviation in regression

The bias of maximum likelihood estimators of the standard deviation of the response in location/scale regression models is considered. Results are obtained for a very wide family of densities for the response variable. These are used to propose point estimators with improved mean square error properties and to demonstrate the importance of bias correction in statistical inference when samples are moderately small.