论文信息 - Bayes linear estimator for two-stage and stratified randomized response models

Bayes linear estimator for two-stage and stratified randomized response models

In this paper, we suggest the Bayes linear estimator (BLE) for randomized response model (RRM) to improve the efficiency of RR estimators, only using the first and second prior moments. The randomized response model is an indirect questioning technique used to protect the privacy of respondents in a survey regarding a sensitive characteristic. Meanwhile Bayes linear estimation is useful for parameter estimation compared to the typical Bayesian method because it only uses the first and second prior knowledge of the variable of interest. Also, it has an advantage of robustness with the distribution. We suggest the Bayes linear estimators for the two-stage and the stratified RRM and find the optimal sample size to minimize the Bayes risk for the stratified RRM. Also, we show the difference in efficiency between the Bayes linear estimators and the typical non-Bayesian RR estimators by simulation study.

Chang-Kyoon Son | Jong-Min Kim | Chang-Kyoon Son | Jong‐Min Kim

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

[2] Bayesian Analysis of Random Response Models. , 1980 .

[3] E. Smouse. A Note on Bayesian Least Squares Inference for Finite Population Models , 1984 .

[4] P. Whittle. On the Smoothing of Probability Density Functions , 1958 .

[5] W. A. Ericson,et al. 9 Bayesian inference in finite populations , 1988 .

[6] Jong-Min Kim,et al. A stratified Warner's randomized response model , 2004 .

[7] Naurang Singh Mangat,et al. An alternative randomized response procedure , 1990 .

[8] Sven A. Eriksson. A New Model for Randomized Response , 1973 .

[9] Anthony O'Hagan,et al. Bayes Linear Estimators for Randomized Response Models , 1987 .

[10] R. Royall. The Linear Least-Squares Prediction Approach to Two-Stage Sampling , 1976 .

[11] J. Hartigan. Linear Bayesian Methods , 1969 .

[12] S. Warner,et al. Respondent Jeopardy and Optimal Designs in Randomized Response Models , 1976 .

[13] P T Liu,et al. The efficiency of the multiple trial randomized response technique. , 1976, Biometrics.

[14] Robert L. Winkler,et al. Warner's Randomized Response Model: A Bayesian Approach , 1979 .

[15] W. R. Simmons,et al. The Unrelated Question Randomized Response Model: Theoretical Framework , 1969 .

[16] M. Stone. Robustness of Non-Ideal Decision Procedures , 1963 .