An alternative to stratified Kim and Warde's randomized response model using optimal (Neyman) allocation

This paper addresses the problem of estimating the population proportion πS 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.

[1]  Sarjinder Singh.  Advanced Sampling Theory with Applications , 2003 .

[2]  Zhimin Hong.  Estimation of mean in randomized response surveys when answers are incompletely truthful , 2006, Model. Assist. Stat. Appl..

[3]  Tae-Young Heo,et al.  On stratified randomized response sampling , 2006, Model. Assist. Stat. Appl..

[4]  Daiho Uhm,et al.  Estimation of a rare sensitive attribute in a stratified sample using Poisson distribution , 2013 .

[5]  Pawan Kumar Mahajan.  Optimum stratification for scrambled response with ratio and regression methods of estimation , 2006, Model. Assist. Stat. Appl..

[6]  I. S. Grewal,et al.  On the relative efficiencies of randomized response devices with Greenberg unrelated question model , 2006, Model. Assist. Stat. Appl..

[7]  An improved two stage randomized response strategy , 1995 .

[8]  Pier Francesco Perri,et al.  Modified randomized devices for Simmons' model , 2008, Model. Assist. Stat. Appl..

[9]  A. Chaudhuri,et al.  Randomized Response: Theory and Techniques , 1987 .

[10]  Jong-Min Kim,et al.  Extensions of Mangat's randomized-response model , 2006 .

[11]  R. K. Gupta,et al.  Optimum stratification for allocation proportional to strata totals for scrambled response , 2007, Model. Assist. Stat. Appl..

[12]  Hwa Young Lee,et al.  A Stratified Randomized Response Technique , 1994 .

[13]  N. S. Mangat,et al.  An Improved Randomized Response Strategy , 1994 .

[14]  A Stratified Unknown Repeated Trials in Randomized Response Sampling , 2012 .

[15]  Matthew E. Elam,et al.  A two-stage stratified Warner’s randomized response model using optimal allocation , 2005 .

[16]  S L Warner,et al.  Randomized response: a survey technique for eliminating evasive answer bias. , 1965, Journal of the American Statistical Association.

[17]  Jong-Min Kim,et al.  A mixed randomized response model , 2005 .

[18]  R. Singh,et al.  Elements of Survey Sampling , 1996 .

[19]  Jingyu Wang,et al.  Ratio imputation method for handling item-nonresponse in Eichhorn model , 2008, Model. Assist. Stat. Appl..