Communications for Statistical Applications and Methods

  • 제28권6호
  • /
  • Pages.643-653
  • /
  • 2021
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Quantile estimation using near optimal unbalanced ranked set sampling

  • Nautiyal, Raman (Department of Statistics, Kumaun University) ;
  • Tiwari, Neeraj (Department of Statistics, Kumaun University) ;
  • Chandra, Girish (Division of Forestry Statistics, Indian Council of Forestry Research and Education)
  • 투고 : 2021.06.04
  • 심사 : 2021.09.28
  • 발행 : 2021.11.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Few studies are found in literature on estimation of population quantiles using the method of ranked set sampling (RSS). The optimal RSS strategy is to select observations with at most two fixed rank order statistics from different ranked sets. In this paper, a near optimal unbalanced RSS model for estimating pth(0 < p < 1) population quantile is proposed. Main advantage of this model is to use each rank order statistics and is distributionfree. The asymptotic relative efficiency (ARE) for balanced RSS, unbalanced optimal and proposed near-optimal methods are computed for different values of p. We also compared these AREs with respect to simple random sampling. The results show that proposed unbalanced RSS performs uniformly better than balanced RSS for all set sizes and is very close to the optimal RSS for large set sizes. For the practical utility, the near optimal unbalanced RSS is recommended for estimating the quantiles.

키워드

참고문헌

  1. Al-Omari AI and Bouza CN (2014). Review of ranked set sampling: modifications and applications, Revista Investigaci 'on Operacional, 35, 215-240.
  2. Barnett V and Moore K (1997). Best linear unbiased estimates in ranked-set sampling with particular reference to imperfect ordering, Journal of Applied Statistics, 24, 697-710. https://doi.org/10.1080/02664769723431
  3. Bhoj DS (1997). New parametric ranked set sampling, Journal of Applied Statistical Sciences, 6, 275-289.
  4. Bhoj DS and Chandra G (2019). Simple unequal allocation procedure for ranked set sampling with skew distributions, Journal of Modern Applied Statistical Methods, 18, eP2811.
  5. Bohn LL and Wolfe DA (1992). Nonparametric two-sample procedures for ranked set samples data, Journal of the American Statistical Association, 87, 552-561. https://doi.org/10.1080/01621459.1992.10475239
  6. Bohn LL and Wolfe DA (1994). The effect of imperfect judgment rankings on properties of procedures based on the ranked-set samples analog of the Mann Whitney-Wilcoxon statistic, Journal of the American Statistical Association, 89, 168--176. https://doi.org/10.1080/01621459.1994.10476458
  7. Chandra G, Bhoj DS, and Pandey R (2018). Simple unbalanced ranked set sampling for mean estimation of response variable of developmental programs, Journal of Modern Applied Statistical Methods, 17.
  8. Chandra G, Tiwari N, and Nautiyal R (2015). Near optimal allocation models for symmetric distributions in ranked set sampling, Statistics in Forestry: Methods and Applications, 85-90.
  9. Chen Z (2000). On ranked set sample quantiles and their applications, Journal of Statistical Planning and Inference, 83, 125-135. https://doi.org/10.1016/S0378-3758(99)00071-3
  10. Chen Z (2001). The optimal ranked set sampling scheme for inference on population quantiles, Statistica Sinica, 11, 23-37.
  11. Cobby JM, Ridout MS, Bassett PJ, and Large RV (1985). An investigation into the use of ranked set sampling on grass and grass-clover swards, Grass and Forage Science, 40, 257-263. https://doi.org/10.1111/j.1365-2494.1985.tb01753.x
  12. David HA and Levine DN (1972). Ranked set sampling in the presence of judgment error, Biometrics, 28, 553--555.
  13. Dell TR and Clutter JL (1972). Ranked set sampling theory with order statistics background, Biometrics, 28, 545--555. https://doi.org/10.2307/2556166
  14. Halls LK and Dell TR (1966). Trials of ranked set sampling for forage yields, Forest Science, 12, 22-26.
  15. Hettmansperger TP (1995). The ranked-set sampling sign test, Nonparametric Statistics, 4, 263-70. https://doi.org/10.1080/10485259508832617
  16. Kaur A, Patil GP, and Taillie C (1997). Unequal allocation models for ranked set sampling with skew distributions, Biometrics, 53, 123-130. https://doi.org/10.2307/2533102
  17. Kaur A, Patil GP, and Taillie C (2000). Optimal allocation for symmetric distributions in ranked sampling, Annals of the Institute of Statistical Mathematics, 52, 239-254. https://doi.org/10.1023/A:1004109704714
  18. Lam K, Sinha BK, and Wu Z (1996). Estimation of location and scale parameters of a logistic distribution using a ranked set sample, Statistical Theory and Applications, Springer, New York.
  19. Latpate R, Kshirsagar J, Gupta VK, and Chandra G (2021). Advanced Sampling Methods, Springer.
  20. Martin WL, Sharik TL, Oderwald RG, and Smith DW (1980). Evaluation of ranked set sampling for estimating shrub phytomass in Appalachian oak forests, Blacksburg, Virginia: School of Forestry and Wildlife Resources, Virginia Polytechnic Institute and State University, FWS, 4-80.
  21. McIntyre GA (1952). A method for unbiased selective sampling using ranked sets, Australian Journal of Agricultural Research, 3, 385-390. https://doi.org/10.1071/AR9520385
  22. Nahhas RW, Wolfe DA, and Chen H (2002). Ranked set sampling: cost and optimal set size, Biometrics, 58, 964-971. https://doi.org/10.1111/j.0006-341X.2002.00964.x
  23. Rohatgi VK and Saleh AK (2000). An introduction to probability and statistics (2nd Ed), John Wiley and Sons.
  24. Stark GV and Wolfe DA (2002). Evaluating ranked-set sampling estimators with imperfect rankings, Journal of Statistical Studies, 77-103.
  25. Stokes SL (1995). Parametric ranked set sampling, Annals of the Institute of Statistical Mathematics, 47, 465-482. https://doi.org/10.1007/bf00773396
  26. Stokes SL and Sager TW (1988). Characterization of a ranked set sample with application to estimating distribution functions, Journal of the American Statistical Association, 83, 374-381. https://doi.org/10.1080/01621459.1988.10478607
  27. Takahasi K and Wakimoto K (1968). On unbiased estimates of the population mean based on the sample stratified by means of ordering, Annals of the Institute of Statistical Mathematics, 20, 1-31. https://doi.org/10.1007/BF02911622
  28. Tiwari N and Chandra G (2011). A systematic approach for unequal allocation for skewed distributions in ranked set sampling, Journal of the Indian Society of Agricultural Statistics, 65, 331-338.
  29. Zhu M and Wang Y (2005). Quantile estimation from ranked set sampling data, Sankhya, 67, 295-304.