Brazilian Journal of Probability and Statistics

Improving mean estimation in ranked set sampling using the Rao regression-type estimator

Elvira Pelle and Pier Francesco Perri

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Abstract

Ranked set sampling is a statistical technique usually used for a variable of interest that may be difficult or expensive to measure, but whose units are simple to rank according to a cheap sorting criterion. In this paper, we revisit the Rao regression-type estimator in the context of the ranked set sampling. The expression of the minimum mean squared error is given and a comparative study, based on simulated and real data, is carried out to clearly show that the considered estimator outperforms some competitive estimators discussed in the recent literature.

Article information

Source
Braz. J. Probab. Stat., Volume 32, Number 3 (2018), 467-496.

Dates
Received: April 2016
Accepted: January 2017
First available in Project Euclid: 8 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1528444868

Digital Object Identifier
doi:10.1214/17-BJPS350

Mathematical Reviews number (MathSciNet)
MR3812378

Zentralblatt MATH identifier
06930035

Keywords
Auxiliary variable order statistics product-type estimators ratio-type estimators bivariate Normal distribution simulation

Citation

Pelle, Elvira; Perri, Pier Francesco. Improving mean estimation in ranked set sampling using the Rao regression-type estimator. Braz. J. Probab. Stat. 32 (2018), no. 3, 467--496. doi:10.1214/17-BJPS350. https://projecteuclid.org/euclid.bjps/1528444868


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References

  • Bouza, C. N. (2008). Ranked set sampling for the product estimator. Revista Investigatión Operacional 29, 201–206.
    Mathematical Reviews (MathSciNet): MR2527997
    Zentralblatt MATH: 1204.62010
  • Chen, Z., Bai, Z. and Sinha, B. K. (2004). Ranked Set Sampling. Theory and Applications. New York: Springer.
    Mathematical Reviews (MathSciNet): MR2151099
    Zentralblatt MATH: 1045.62007
  • David, H. A. and Nagaraja, H. N. (2003). Order Statistics, 3rd ed. Hoboken, New Jersey: John Wiley & Sons, Inc.
    Mathematical Reviews (MathSciNet): MR1994955
    Zentralblatt MATH: 1053.62060
  • Diana, G. and Perri, P. F. (2007). Estimation of finite population mean using multi-auxiliary information. Metron LXV, 99–112.
  • Jeelani, M. I. and Bouza, C. N. (2015). New ratio method of estimation under ranked set sampling. Revista Investigación Operational 36, 151–155.
  • Kadilar, C., Unyazici, Y. and Cingi, H. (2009). Ratio estimator for the population mean using ranked set sampling. Statistical Papers 50, 301–309.
    Zentralblatt MATH: 1309.62023
    Digital Object Identifier: doi:10.1007/s00362-007-0079-y
  • McIntyre, G. A. (1952). A method for unbiased selective sampling using ranked set sampling. Australian Journal of Agricultural Research 3, 385–390. DOI:10.1071/AR9520385.
  • Mehta (Ranka), N. and Mandowara, V. L. (2016). A modified ratio-cum-product estimator of finite population mean using ranked set sampling. Communications in Statistics Theory and Methods 45, 267–276.
    Zentralblatt MATH: 1337.62022
    Digital Object Identifier: doi:10.1080/03610926.2013.830748
  • Prasad, B. (1989). Some improved ratio type estimators of population mean and ratio in finite population sample surveys. Communications in Statistics Theory and Methods 18, 379–392.
    Zentralblatt MATH: 0696.62012
    Digital Object Identifier: doi:10.1080/03610928908829905
  • Rao, T. J. (1991). On certain methods of improving ratio and regression estimators. Communications in Statistics Theory and Methods 20, 3325–3340.
    Zentralblatt MATH: 0800.62046
    Digital Object Identifier: doi:10.1080/03610929108830705
  • Samawi, H. M. and Muttlak, H. A. (1996). Estimation of ratio using rank set sampling. Biometrical Journal 6, 753–764.
    Zentralblatt MATH: 0929.62005
    Digital Object Identifier: doi:10.1002/bimj.4710380616
  • Singh, H. P., Tailor, R., Tailor, R. and Kakran, M. S. (2004). An improved estimator of population means using power transformation. Journal of the Indian Society of Agricultural Statistics 58, 223–230.
    Zentralblatt MATH: 1188.62040
  • Sisodia, B. V. S. and Dwivedi, V. K. (1981). A modified ratio estimator using coefficient of variation of auxiliary variable. Journal of the Indian Society of Agricultural Statistics 33, 13–18.
  • Stokes, S. L. (1997). Ranked set sampling with concomitant variables. Communications in Statistics Theory and Methods 6, 1207–1211. DOI:10.1080/03610927708827563.
  • Tailor, R. and Sharma, B. (2009). A modified ratio-cum-product estimator of finite population mean using known coefficient of variation and coefficient of kurtosis. Statistics in Transition—New Series 10, 15–24.
  • Upadhyaya, L. N. and Singh, H. P. (1999). Use of transformed auxiliary variable in estimating the finite population mean. Biometrical Journal 41, 627–636.
    Zentralblatt MATH: 0963.62014
    Digital Object Identifier: doi:10.1002/(SICI)1521-4036(199909)41:5<627::AID-BIMJ627>3.0.CO;2-W
  • Yu, P. L. H. and Lam, K. (1997). Regression estimator in ranked set sampling. Biometrics 53, 1070–1080. DOI:10.2307/2533564.

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