Ki-Hak Hong

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.

An Additive Stratified Quantitative Attribute Randomized Response Model

Abstract For a sensitive survey in which the population is composed by several strata with quantitative attributes,we present an additive stratified quantitative attribute randomized response model which applied stratifiedrandom sampling instead of simple random sampling to the models of Himmelfarb-Edgell’s additive quanti-tative attribute model and Gjestvang-Singh’s. We also establish theoretical grounds to estimate the stratummean of sensitive quantitative attributes as well as the over all mean. We deal with the proportional andoptimal allocation problems in each suggested model and compare the relative efficiency of the suggestedtwo models; subsequently, Himmelfarb-Edgell’s model is more efficient than Gjestvang-Singh’s model underthe condition of stratified random sampling.Keywords: Additive randomized response model, quantitative attribute, stratified sampling, sample alloca-tion. 1. 서론 Warner (1965)가 응답자들의 신분이나 사생활을 보호할 수 있는 확률장치를 통해 민감한 속성의 모비율을 추정할 수 있는 확률화응답모형을 처음으로 제안한 이후 많은 연구자들이 모집단내 민감한 속성을추정하기 위한 연구로서Warner모형을 발전시켜 왔다.특히, Himmelfarb와 Edgell (1980)은 민감한 양적인 변수의 정보를 얻기 위하여 가법 모형(additivemodel)을 제안하였다. 이와 같은 가법 모형은 응답자들에게 자신들의 응답에 변환된 변수를 사용하여개인적인 민감한 정보를 보호하도록 하고 있다. 즉, 민감한 변수

An Dynamic Optimal Allocation for the Stratified Randomized Response Technique

Typically the standard optimal allocation method distributes the sample for each stratum considering survey cost. In case of varying survey cost for each survey unit, we need to consider more practical allocation method. In other words, according to characteristics of an individual unit, we consider the optimal dynamic allocation method which first selects the survey unit having maximum value of benefit cost ratio. In terms of this, the proposed allocation method is different from standard optimal allocation method which allocate samples for each stratum and selects the random sample according to each size of sample. This paper is considered the dynamic optimal allocation method for the stratified randomized response technique which surveys for sensitive characteristic of survey units such as drug abuse, abortion, alcoholic. We prove the practical usefulness of proposed method using the numerical example.