Zawar HUSSAİN, Javid SHABBİR, Naila SHABBİR

An alternative item sum technique for improved estimators of population mean in sensitive surveys

The item sum technique (IST) was developed for the measurement of quantitative sensitive variables. This method is closely related to the unmatched count technique (UCT), which was developed to measure the proportion of dichotomous sensitive items in a human populationsurveys. In this article, firstly, we proposed an improved IST which has a fruitful advantage that it does not require two subsamples as in usual IST and there is also no need of finding optimum subsample sizes. We derived the mean and variance of the proposed estimator and compare it with the usual IST both theoretically and numerically. Secondly, we suggest some alternative family of estimators of the population mean of sensitive variable and compare them with estimator, based on the proposed one sample version of IST. Thirdly, we utilize auxiliary information in estimation of population mean, say $\mu_s$ of sensitive variable. It is established that the estimator based on the proposed IST is always more efficient than its usual counterpart. The estimator using second raw moment of the auxiliary variable is observed to be more efficient than the other auxiliary information based estimators, namely, the ratio, product and regression estimators. The usual and proposed ISTs are applied to estimate the average number of classes missed by the student during the last semester at the Quaid-i-Azam University. Estimated average of number of missed classes and 95% confidence intervals are reported showing that the proposed IST yields precise estimates compared to the usual IST.

Keywords:

auxiliary information item sum technique, sensitive variable, unmatched count technique,

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Chang, H.-J., Wang, C.-L., Huang, K.-C. Using randomized response to estimate the proportion and truthful reporting probability in a dichotomous nite population, Journal of Applied Statistics 31 (5), 565573, 2004.
Chaudhuri, Arijit.Randomized response and indirect questioning techniques in sur- veys, CRC Press, 2010..
Chaudhuri, A. and Christodes, T. C. Item count technique in estimating the propor- tion of people with a sensitive feature, Journal of Statistical Planning and Inference 137 (2), 589593, 2007.
Christodes, T.C. A generalized randomized response technique. Metrika, 57 (2), 195200, 2003.
Cochran,W.G. The Estimation of the Yields of the Cereal Experiments by Sampling for the Ratio of Grain to Total Produce , The Journal of Agric Science 30(2), 262- 275, 1940.
Coutts, E. and Jann, B. Sensitive questions in online surveys: Experimental results for the randomized response technique and the unmatched count technique (UCT), Sociological Methods & Research 40 (1), 169193, 2011.
Dalton, D.R., Wimbush, J.C. and Daily, C.M. Using the unmatched count technique (UCT) to estimate base rates for sensitive behavior, Personnel Psychology 47 (4), 817829, 1994.
Dalton, D.R., Daily, C.M. and Wimbush, J.C. Collecting sensitive data in busi- ness ethics research: A case for the unmatched count technique (UCT), Journal of Business Ethics 16(10), 10491057, 1997.
Diana, G., & Perri, P. F. Estimating a sensitive proportion through randomized response procedures based on auxiliary information, Statistical Papers 50 (3), 661- 672, 2009.
Diana, G. and Perri, P. F. New Scrambled response models for estimating the mean of a sensitive character, Journal of Applied Statistics 37 (11), 1875-1890, 2010.
Droitcour, J., Caspar, R. A., Hubbard, M. L., Parsley, T. L., Visscher, W., & Ezzati, T. M.The item count technique as a method of indirect questioning: A review of its development and a case study application, Measurement errors in surveys, 185-210, 1991.
Droitcour, Judith A., Eric M. Larson, and Fritz J. Scheuren. The three card method: Estimating sensitive survey items with permanent anonymity of response, in Pro- ceedings of the Social Statistics Section, American Statistical Association, Alexan- dria, Virginia 2001.
Geurts, M. D. Using a randomized response research design to eliminate non- response and response biases in business research, Journal of the Academy of Mar- keting Science 8 (1-2), 83-91, 1980.
Gilens, M., Sniderman, P.M. and Kuklinski, J.H. . Armative action and the politics of realignment, British Journal of Political Science 28 (1), 159183, 1998.
Gjestvang, C. R., & Singh, S. A new randomized response model, Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68 (3), 523-530, 2006.
Greenberg, B. G., Abul-Ela, A. L. A., Simmons, W. R., & Horvitz, D. G. The unrelated question randomized response model: Theoretical framework, Journal of the American Statistical Association 64 (326), 520-539, 1969.
Gupta, S., Mehta, S., Shabbir, J., & Dass, B. K. Generalized scrambling in quan- titative optional randomized response models, Communications in Statistics-Theory and Methods 42 (22), 4034-4042, 2013.
Horvitz, D.G., Shah, B.V., Simmons,W.R. (1967). The unrelated question RR model, in Proceedings of the Social Statistics Section of the American Statistical Association (pp. 6572). Alexandria, VA: ASA.
Hubbard, M. L., Casper, R. A. & Lessler, J. T. Respondents' reactions to item count lists and randomized response, in Proceedings of the Survey Research Section, American Statistical Association, Washington, D. C., pp. 544448, 1989.
Hussain, Z., Shabbir, J. An estimation of sensitive proportion utilizing higher order moments of auxiliary variable , International Journal of Business and Social Science 2 (2), 121-125, 2011.
Hussain, Z., Shah, E. A. and Shabbir, J. An alternative item count technique in sensitive surveys, Revista Colombiana de Estadistica 35 (1), 3954, 2012.
Janus, A.L. The inuence of social desirability pressures on expressed immigration attitudes, Social Science Quarterly 91 (4), 928 946, 2010.
Kim, J. M., and Warde, W. D. A stratied Warner's randomized response model, Journal of Statistical Planning and Inference 120 (1), 155-165, 2004.
Kuk, A.Y.C. Asking sensitive questions indirectly, Biometrika 77 (2), 436438, 1990.
Kuklinski, J.H., Cobb, M.D. and Gilens, M. Racial attitudes and the new south, Journal of Politics 59 (2), 323349, 1997.
Mangat, N.S., & Singh, R. An alternative randomized response procedure, Biometrika 77 (2), 439442, 1990.
Mangat, N. S. An improved randomized response strategy, Journal of the Royal Statistical Society. Series B (Methodological), 93-95, 1994.
Mathur, N. and Singh, H.P . Estimation of population mean with prior information using scrambled response technique, Brazilian Journal of Probability and Statistics 22 (2), 165 181, 2008.
Mehta, S., Dass, B. K., Shabbir, J., & Gupta, S. N. A three-stage optional ran- domized response model, Journal of Statistical Theory and Practice 6 (3), 417427, 2012.
Miller, J. D. A new survey technique for studying deviant behavior. University Mi- crolms, 1984.
Miller, J. D. The nominative technique: A new method of estimating heroin preva- lence, NIDA Research Monograph 54, 104-124, 1985.
Murthy, M.N . Product method of estimation, Sankhy d , A, 26, 6974, 1964.
Rayburn, N.R., Earleywine, M. and Davison, G.C. Base rates of hate crime victimization among college students, Journal of Interpersonal Violence 18 (10), 12091221, 2003.
Searls, D. T. The utilization of a known coecient of variation in the estimation procedure, Journal of the American Statistical Association 59(308), 12251226, 1964.
Smith, L. L., Federer, W. T., & Raghavarao, D. A comparison of three techniques for eliciting truthful answers to sensitive questions, In Proceedings of the Social Statistics Section, American Statistical Association (pp. 447-52), 1974.
Thompson, J. R. Some shrinkage techniques for estimating the mean, Journal of the American Statistical Association 63 (321), 113-122, 1968.
Tsuchiya, T., Hirai, Y. and Ono, S. A study of the properties of the item count technique, Public Opinion Quarterly 71 (2), 253272, 2007.
Trappmann, M., Krumpal, I., Kirchner, A., &Jann, B. Item sumA new technique for asking quantitative sensitive questions, Journal of Survey Statistics and Method- ology 2 (1), 5877, 2014.
Warner, S. L. Randomized response: A survey technique for eliminating evasive answer bias, Journal of the American Statistical Association 60(309), 63 69, 1965.
Zaizai, Y. Ratio method of estimation of population proportion using randomized device technique, Model Assisted Statistics and Application 1 (2), 125-130, 2006.