Gi-Sung Lee

Estimation of a rare sensitive attribute in a stratified sample using Poisson distribution

This study proposes the estimators for the mean and its variance of the number of respondents who possessed a rare sensitive attribute based on stratified sampling schemes (stratified sampling and stratified double sampling). This study deals with the extension of the estimation reported in Land et al. [Estimation of a rare sensitive attribute using Poisson distribution, Statistics (2011), in press. DOI: 10.1080/02331888.2010.524300] using a Poisson distribution and an unrelated question randomized response model reported in Greenberg et al. [The unrelated question randomized response model: Theoretical framework, J. Amer. Statist. Assoc. 64 (1969), 520–539]. In the stratified sampling, the estimators are proposed when the parameter of the rare unrelated attribute is known and unknown. The variances of estimators using a proportional and optimum allocation are also suggested. The proposed estimators are evaluated using a relative efficiency comparing variances of the estimators reported in Land et al. depending on the parameters and the probability of selecting a question. We showed that our proposed methods have better efficiencies than Land et al.’s randomized response model in some conditions. When the sizes of stratified populations are not given, other estimators are suggested using a stratified double sampling. For the proportional allocation, the difference between two variances in the stratified sampling and the stratified double sampling is given with the known rare unrelated attribute.

Estimation of a rare sensitive attribute in probability proportional to size measures using Poisson distribution

We propose new variants of Land et al.’s [Estimation of a rare sensitive attribute using Poisson distribution. Statistics. 2011. DOI: 10.1080/02331888.2010.524300] randomized response model when a population consists of some clusters and the population is stratified with some clusters in each stratum. The estimator for the mean number of persons who possess a rare sensitive attribute, its variance, and the variance estimator are suggested when the parameter of a rare unrelated attribute is assumed to be known and unknown. The clusters are selected with and without replacement. When they are selected with replacement, the selecting probabilities for each cluster are defined depending on the cluster sizes and with equal probability. In addition, the variance comparison between a probability proportional to size (PPS) and PPS for stratification are performed. When the parameters vary in clusters, the stratified PPS has better efficiency than the PPS.

The Calibration for Stratified Randomized Response Estimators

In this paper, we propose the calibration procedure for the valiance reduction of the stratified Warners randomized response estimators, which suggested by Hong et al. (1994) and Kim and Warde (2004), using auxiliary information at the population level. It is shown that the proposed calibration estimators are more efficient than the ordinary Warners estimators.

An estimation of a sensitive attribute by two stage stratified randomized response model

We deal with the estimation of sensitive attributeof the population which is composed of a number of strata by applying stratified sampling to Abdelfatah et al.s model (1). We estimate the sensitive parameter in the case of knowing the size of stratum, and check the effect of the proportional allocation method and the optimum allocation method. We extend it to the case of not knowing the size of stratum, and estimate the sensitive parameter by applying stratified double sampling to Abdelfatah et al.s model (1). Finally, we compare the efficiency of our suggested estimator to the existing Abdelfatah et al.s estimator. A practical problem with the use of optimum allocation has been pointed out. Thus, in practice, the use of either proportional allocation or equal allocation has been suggested while estimating proportion of a sensitive attribute using stratified randomized response sampling.

Estimation of the proportion of a sensitive attribute based on a two-stage randomized response model with stratified unequal probability sampling

To estimate the proportion of a sensitive attribute of the population that is composed of the number of different sized clusters, we suggest a two-stage randomized response model with unequal probability sampling by using Abdelfatah et al.’s procedure [Braz. J. Probab. Stat. 27 (2013) 608– 617]. We compute the estimate of the sensitive parameter, its variance, and the variance estimator for both pps sampling and two-stage equal probability sampling. We extend our model to the case of stratified unequal probability sampling and compute them. Finally, we compare the efficiency of the two estimators, one obtained by unequal probability sampling and the other by stratified unequal probability sampling.

A stratified two-stage unrelated randomized response model for estimating a rare sensitive attribute based on the Poisson distribution

This article estimates the mean number of individuals with a rare sensitive attribute by using the Poisson distribution and stratified two-stage sampling and extends the Land et al. model to a stratified population. A rare sensitive parameter is estimated for the case in which stratum size is known, and proportional and optimal allocation methods are taken into account. We extended the Land et al. model to the case of an unknown stratum size; a rare sensitive parameter is estimated by applying stratified double sampling to the Land et al. model, and these two allocation methods are checked. Finally, the efficiency of the proposed model is compared with that of Land et al. in terms of the estimator variance.

The Three-Stage Stratified Unrelated Question Model

For procuring more sensitive information and estimating stratum target population proportion as well as an overall one form a sensitive population composed of several strata we suggest a two-stage stratified unrelated question model that uses stratified random sampling instead of simple random sampling in the two-stage unrelated question model by Kim et al. (1992) and extend it to the three-stage stratified unrelated question model. We also deal with the proportional and optimal allocation problems in each suggested model, compare the relative efficiency of the suggested two models, and show that the three-stage stratified unrelated question model is more efficient than the two-stage one in view of the variance.

The Calibration for Two-Phase Randomized Response Estimator

This article presents the calibration procedure of the two-phase randomized response (RR) technique for surveying the sensitive characteristic. When the sampling scheme is two-phase or double sampling, auxiliary information known from the entire population can be used, but the auxiliary information should be information available from both the first and second phases of the sample. If there is auxiliary information available from both the first and second phases, then we can improve the ordinary two-phase RR estimator by incorporating this information in the estimation procedure. In this article, we used the new two-step Newtons method for computing unknown constants in the calibration procedure and compared the efficiency of the proposed estimator through some numerical study.

Calibration for Randomized Response Estimators

In the present article, we consider the calibration procedure for the Warners and Mangat–Singhs (:M–S) randomized response survey estimators using auxiliary information associated with the variable of interest. In the calibration procedure, we can use auxiliary information such as age, gender, and income for the respondents of RR questions from an external source, and then the classical RR estimators can be improved with respect to the problems of noncoverage or nonresponse. From the efficiency comparison study, we show that the calibration estimators are more efficient than those of Warners and Mangat-Singhs when the known population cell and marginal counts of auxiliary information are used for the calibration procedure.

A new stratified three-stage unrelated randomized response model for estimating a rare sensitive attribute based on the Poisson distribution

ABSTRACT This article suggests an efficient method of estimating a rare sensitive attribute which is assumed following Poisson distribution by using three-stage unrelated randomized response model instead of the Land et al. model (2011) when the population consists of some different sized clusters and clusters selected by probability proportional to size(:pps) sampling. A rare sensitive parameter is estimated by using pps sampling and equal probability two-stage sampling when the parameter of a rare unrelated attribute is assumed to be known and unknown. We extend this method to the case of stratified population by applying stratified pps sampling and stratified equal probability two-stage sampling. An empirical study is carried out to show the efficiency of the two proposed methods when the parameter of a rare unrelated attribute is assumed to be known and unknown.