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A pseudo-empirical log-likelihood estimator using scrambled responses

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  • Singh, Sarjinder
  • Kim, Jong-Min

Abstract

In this paper, we propose an empirical log-likelihood estimator for estimating the population mean of a sensitive variable in the presence of an auxiliary variable. A new concept of conditional mean squared error of the empirical likelihood estimator is introduced. The proposed method is valid for simple random and without replacement sampling (SRSWOR) and could easily be extended for complex survey designs. The relative efficiency of the proposed pseudo-empirical log-likelihood estimator with respect to the usual, and to a recent estimator due to Diana and Perri (2009b), has been investigated through a simulation study.

Suggested Citation

  • Singh, Sarjinder & Kim, Jong-Min, 2011. "A pseudo-empirical log-likelihood estimator using scrambled responses," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 345-351, March.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:3:p:345-351
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    References listed on IDEAS

    as
    1. Christopher Gjestvang & Sarjinder Singh, 2007. "Forced quantitative randomized response model: a new device," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(2), pages 243-257, September.
    2. Wu C. & Sitter R. R, 2001. "A Model-Calibration Approach to Using Complete Auxiliary Information From Survey Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 185-193, March.
    3. Montanari, Giorgio E. & Ranalli, M. Giovanna, 2005. "Nonparametric Model Calibration Estimation in Survey Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1429-1442, December.
    4. M. Rueda & J. Muñoz & Y. Berger & A. Arcos & S. Martínez, 2007. "Pseudo empirical likelihood method in the presence of missing data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(3), pages 349-367, May.
    5. Giancarlo Diana & Pier Perri, 2009. "Estimating a sensitive proportion through randomized response procedures based on auxiliary information," Statistical Papers, Springer, vol. 50(3), pages 661-672, June.
    6. Derrick Shannon Tracy & Sarjinder Singh, 1999. "Calibration estimators in randomized response surveys," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 47-68.
    7. Shaul K. Bar-Lev & Elizabeta Bobovitch & Benzion Boukai, 2004. "A note on randomized response models for quantitative data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(3), pages 255-260, November.
    8. Sarjinder Singh & Derrick Shannon Tracy, 1999. "Ridge regression using scrambled responses," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 147-157.
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    Cited by:

    1. Giancarlo Diana & Pier Francesco Perri, 2012. "A calibration-based approach to sensitive data: a simulation study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 53-65, March.

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