Model Assisted Statistics and Applications - Volume 9, issue 1

Authors: Singh, Sarjinder

Article Type: Editorial

DOI: 10.3233/MAS-130281

Citation: Model Assisted Statistics and Applications, vol. 9, no. 1, pp. 1-2, 2014

Authors: Barabesi, Lucio | Diana, Giancarlo | Perri, Pier Francesco

Article Type: Research Article

Abstract: We consider the nonstandard situation where the randomized response theory is applied in a nonresponse set-up. The customary Horvitz-Thompson estimator for the population total of a sensitive variable is adjusted to take into account missing data, true response and randomized response, and the expression of its variance and the corresponding estimator provided. Finally, a numerical study is carried out to investigate how the estimation process can be affected by scrambled responses and how possible improvements in respondent cooperation can compensate for certain levels of nonresponse.

Keywords: Horvitz-Thompson estimator, multiplicative model, relative efficiency loss, variance estimator

DOI: 10.3233/MAS-130274

Citation: Model Assisted Statistics and Applications, vol. 9, no. 1, pp. 3-10, 2014

Authors: Quatember, Andreas

Article Type: Research Article

Abstract: Nonresponse and untruthful answers cause serious problems in sample and population surveys on sensitive variables. In this article, firstly, the idea of Liu and Chow [15] for the estimation of relative sizes of different categories applicable in the field of opinion polls is explicated for complex sampling designs. Secondly, in the case that the moment estimator lies outside the parameter space a Maximum Likelihood solution is presented along with a method to allow the calculation of confidence intervals. Thirdly, the privacy protection offered by the method is discussed. A concluding simulation study allows a look on the effect of the …usage of this questioning design from different aspects. Show more

Keywords: Sampling theory, survey methodology, EM algorithm, bootstrap, opinion polls, voting behavior

DOI: 10.3233/MAS-130275

Citation: Model Assisted Statistics and Applications, vol. 9, no. 1, pp. 11-23, 2014

Authors: Hong, Ki-Hak | Lee, Gi-Sung | Son, Chang-Kyoon | Kim, Jong-Min

Article Type: Research Article

Abstract: We deal with the estimation of sensitive attribute of 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. Show more

Keywords: Randomized response model, two-stage model, sensitive attribute, stratified sampling, stratified double sampling

DOI: 10.3233/MAS-130276

Citation: Model Assisted Statistics and Applications, vol. 9, no. 1, pp. 25-35, 2014

Authors: Singh, Housila P. | Tarray, Tanveer A.

Article Type: Research Article

Abstract: This paper addresses the problem of estimating the population proportion π S possessing the sensitive attribute using stratified random sampling. Two alternatives to Kim and Warde [12] stratified randomized response model have been proposed. The proposed models are based on extending Singh [28] models to the case of stratified random sampling. It has been shown that the proposed models are more efficient than Kim and Warde [12] stratified randomized response technique under some realistic conditions in both the cases of completely truthful reporting and that of not completely truthful reporting by the respondents. A …practical problem with the use of optimum (Neyman) 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. Numerical illustrations and graphs are also given in support of the present study. Show more

Keywords: Randomized response technique, stratified random sampling, dichotomous population, sensitive attribute, estimation of proportion, bias, mean square error

DOI: 10.3233/MAS-130277

Citation: Model Assisted Statistics and Applications, vol. 9, no. 1, pp. 37-62, 2014

Authors: Abdelfatah, Sally | Mazloum, Reda

Article Type: Research Article

Abstract: Odumade and Singh [10] have extended the Warner randomized response model [15] by the use of two decks of cards. In this paper, a new randomized response model based on the use of three decks of cards is proposed as an extension to the Odumade and Singh model [10]. The Cramer-Rao lower bound of the variance of the proposed estimator has been obtained. An empirical study has also been performed to compare the lower bound of the variance of the new estimator with that developed by Singh and Sedory [14]. The new estimator turned out to be more efficient than …the Singh and Sedory estimator [14] but the problem of low level of respondents' cooperation can be accompanied with the new model. In an attempt to maintain the respondents' privacy and thereby increase the level of their cooperation, another model using three decks of cards was suggested. When comparing the two proposed models, it was found that the second model can be easily adjusted to be more efficient than the first model; moreover it can largely increase the respondents' cooperation as there is a chance that the respondent will answer the sensitive question only once or twice. Show more

Keywords: Simple random sampling, estimation of proportion, randomized response technique, three decks of cards, maximum likelihood estimation

DOI: 10.3233/MAS-130278

Citation: Model Assisted Statistics and Applications, vol. 9, no. 1, pp. 63-72, 2014

Authors: Singh, Housila P. | Tarray, Tanveer A.

Article Type: Research Article

Abstract: The quest of this paper is to propose an improved mixed randomized response model for estimating the proportion of sensitive attribute π S in the population. Mangat et al. [17] and Singh et al. [28] pointed out the privacy problem with the Moors [18] model. However their models may lose a large portion of data information and require a high cost to obtain confidentiality of the respondents as pointed by Kim and Warde’s [11]. This led Kim and Warde’s [11] to propose a mixed randomized response model using simple random sampling which rectifies the …privacy problem. In this paper we have suggested a mixed randomized response model using Mangat and Singh [13] two – stage randomized response technique in place of second randomization device in Kim and Warde mixed randomized response model where they have used exactly the Warner’s randomized response model. It has been shown that the proposed mixed randomized response model is better than Kim and Warde’s [11] mixed randomized response model. Numerical illustration is given in support of the present study. The proposed model has been also extended in stratified sampling. Show more

Keywords: Randomized response technique, dichotomous population, estimation of proportion, privacy of respondents, sensitive characteristics

DOI: 10.3233/MAS-130279

Citation: Model Assisted Statistics and Applications, vol. 9, no. 1, pp. 73-87, 2014

Authors: Sidhu, S.S. | Grewal, I.S. | Javed, M.

Article Type: Research Article

Abstract: In this paper, the scrambled and forced response method was used as the randomized response technique to maximize the efficiency of randomized response designs. When randomized response designs become more efficient their value as a tool to study sensitive topics will increase. An overview of the literature shows that when sensitive or incriminating topics are studied, the overall results of randomized response studies are more valid than the results of direct question designs. We propose a set of alternative estimators for probability proportional to size with replacement (PPSWR) corresponding to multi-character survey that elicit simultaneous information on many sensitive study …variables. The estimators proposed are all biased but it is expected that the extent of bias will be smaller, since the proposed estimators are suitable for situations in between those optimum for the usual estimators and the estimators based on multi-characters for no correlation. The Mean Square Error (MSE) expressions are derived for the proposed estimators. The behavior of the proposed estimator has been examined under super population model. Numerical illustrations are carried out to show the performance of the proposed estimator model under forced response model. Show more

Keywords: Total estimation, randomized response, forced response, sensitive multi-characteristics, mean square error, super population model

DOI: 10.3233/MAS-130280

Citation: Model Assisted Statistics and Applications, vol. 9, no. 1, pp. 89-96, 2014