×

Ratio estimation of the mean of a sensitive variable in the presence of auxiliary information. (English) Zbl 05902629

Summary: We propose a ratio estimator for the mean of sensitive variable utilizing information from a nonsensitive auxiliary variable. Expressions for the Bias and MSE of the proposed estimator (correct up to first and second order approximations) are derived. We show that the proposed estimator does better than the ordinary RRT mean estimator that does not utilize the auxiliary information. We also show that there is hardly any difference in the first order and second order approximations for MSE even for small sample sizes. We also generalize the proposed estimator to the case of transformed ratio estimators but these transformations do not result in any significant reduction in MSE. An extensive simulation study is presented to evaluate the performance of the proposed estimator. The procedure is also applied to some financial data (purchase orders (sensitive variable) and gross turn-over (non-sensitive variable)) in 2009 for 5090 companies in Portugal from a survey on Information and Communication Technologies (ICT) usage.

MSC:

62-XX Statistics
Full Text: DOI

References:

[1] Chandra P., Statistics in Transition 7 (1) pp 27– (2005)
[2] Eichhron B. H., Journal of Statistical Planning and Inference 7 pp 307– (1983) · doi:10.1016/0378-3758(83)90002-2
[3] Official Publications of the European Communities pp 112– (2008)
[4] DOI: 10.1016/S0378-3758(01)00137-9 · Zbl 0985.62010 · doi:10.1016/S0378-3758(01)00137-9
[5] Gupta S., Statistica 64 pp 643– (2004)
[6] Gupta S., Journal of Statistical Planning and Inference 140 (10) pp 2870– (2010) · Zbl 1191.62009 · doi:10.1016/j.jspi.2010.03.010
[7] DOI: 10.1016/j.aml.2005.02.039 · Zbl 1125.62002 · doi:10.1016/j.aml.2005.02.039
[8] Koyuncy N., Hacettepe Journal of Mathematics and Statistics 38 (2) pp 217– (2009)
[9] Kulkarni S. P., Journal of the Indian Society of Agricultural Statistics 30 (2) pp 125– (1977)
[10] Saha A., Journal of Statistical Theory and Practice 2 (4) pp 589– (2008) · Zbl 1211.62023 · doi:10.1080/15598608.2008.10411897
[11] Shabbir J., Hacettepe Journal of Mathematics and Statistics 39 (1) pp 121– (2010)
[12] Singh H. P., Journal of Statistical Theory and Practice 2 (1) pp 21– (2008) · doi:10.1080/15598608.2008.10411858
[13] DOI: 10.1007/BF02479358 · Zbl 0337.62018 · doi:10.1007/BF02479358
[14] Sisodia B. V.S., Journal of the Indian Society of Agricultural Statistics 33 pp 13– (1981)
[15] Smilhily M., Eurostat Publications (2010)
[16] Sukhatme P. V., Sampling Theory of Surveys with Applications (1970) · Zbl 0239.62008
[17] Turgut Y., Hacettepe Journal of Mathematics and Statistics 37 (2) pp 177– (2008)
[18] DOI: 10.1002/(SICI)1521-4036(199909)41:5<627::AID-BIMJ627>3.0.CO;2-W · Zbl 0963.62014 · doi:10.1002/(SICI)1521-4036(199909)41:5<627::AID-BIMJ627>3.0.CO;2-W
[19] Upadhyaya L. N., Statistics in Transition 4 (6) pp 1019– (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.