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Improving the best linear unbiased estimator for the scale parameter of symmetric distributions by using the absolute value of ranked set samples

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  • Gang Zheng
  • Mohammad Al-Saleh

Abstract

Ranked set sampling is a cost efficient sampling technique when actually measuring sampling units is difficult but ranking them is relatively easy. For a family of symmetric location-scale distributions with known location parameter, we consider a best linear unbiased estimator for the scale parameter. Instead of using original ranked set samples, we propose to use the absolute deviations of the ranked set samples from the location parameter. We demonstrate that this new estimator has smaller variance than the best linear unbiased estimator using original ranked set samples. Optimal allocation in the absolute value of ranked set samples is also discussed for the estimation of the scale parameter when the location parameter is known. Finally, we perform some sensitivity analyses for this new estimator when the location parameter is unknown but estimated using ranked set samples and when the ranking of sampling units is imperfect.

Suggested Citation

  • Gang Zheng & Mohammad Al-Saleh, 2003. "Improving the best linear unbiased estimator for the scale parameter of symmetric distributions by using the absolute value of ranked set samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 253-265.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:3:p:253-265
    DOI: 10.1080/0266476022000030039
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    References listed on IDEAS

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    1. Emad El-Neweihi & Bikas K. Sinha, 2000. "Reliability estimation based on ranked set sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 29(7), pages 1583-1595, January.
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    3. Amarjot Kaur & G. Patil & C. Taillie, 2000. "Optimal Allocation for Symmetric Distributions in Ranked Set Sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 239-254, June.
    4. Lynne Stokes, 1995. "Parametric ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 465-482, September.
    5. Vic Barnett & Karen Moore, 1997. "Best linear unbiased estimates in ranked-set sampling with particular reference to imperfect ordering," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(6), pages 697-710.
    6. M. S. Ridout & J. M. Cobby, 1987. "Ranked Set Sampling with Non‐Random Selection of Sets and Errors in Ranking," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(2), pages 145-152, June.
    7. Gang Zheng & Mohammad Al-Saleh, 2002. "Modified Maximum Likelihood Estimators Based on Ranked Set Samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 641-658, September.
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    1. Hani M. Samawi & Haresh Rochani & Daniel Linder & Arpita Chatterjee, 2017. "More efficient logistic analysis using moving extreme ranked set sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 753-766, March.

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