DOI QR코드

DOI QR Code

Nonparametric confidence intervals for quantiles based on a modified ranked set sampling

  • Morabbi, Hakime (Department of Statistics, Ferdowsi University of Mashhad) ;
  • Razmkhah, Mostafa (Department of Statistics, Ferdowsi University of Mashhad) ;
  • Ahmadi, Jafar (Department of Statistics, Ferdowsi University of Mashhad)
  • 투고 : 2015.08.08
  • 심사 : 2016.02.03
  • 발행 : 2016.03.31

초록

A new sampling method is introduced based on the idea of a ranked set sampling scheme in which taken samples in each set are dependent on previous ones. Some theoretical results are presented and distribution-free confidence intervals are derived for the quantiles of any continuous population. It is shown numerically that the proposed sampling scheme may lead to 95% confidence intervals (especially for extreme quantiles) that cannot be found based on the ordinary ranked set sampling scheme presented by Chen (2000) and Balakrishnan and Li (2006). Optimality aspects of this scheme are investigated for both coverage probability and minimum expected length criteria. A real data set is also used to illustrate the proposed procedure. Conclusions are eventually stated.

키워드

참고문헌

  1. Al-Saleh MF and Al-Omari AI (2002). Multistage ranked set sampling, Journal of Statistical Planning and Inference, 102, 273-286. https://doi.org/10.1016/S0378-3758(01)00086-6
  2. Al-Saleh MF and Samawi H (2010). On estimating the odds using moving extreme ranked set sampling, Statistical Methodology, 7, 133-140. https://doi.org/10.1016/j.stamet.2009.11.004
  3. Balakrishnan N and Li T (2006). Confidence intervals for quantiles and tolerance intervals based on ordered ranked set samples, Annals of the Institute of Statistical Mathematics, 58, 757-777. https://doi.org/10.1007/s10463-006-0035-y
  4. Barnett V (1999). Ranked set sample design for environmental investigations, Environmental and Ecological Statistics, 6, 59-74. https://doi.org/10.1023/A:1009643517647
  5. 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
  6. Castillo E, Hadi AS, Balakrishnan N, and Sarabia JM (2005). Extreme Value and Related Models with Applications in Engineering and Science, John Wiley & Sons, New York.
  7. Chahkandi M, Ahmadi J, and Baratpour S (2014). Non-parametric prediction intervals for the lifetime of coherent systems, Statistical Papers, 55, 1019-1034. https://doi.org/10.1007/s00362-013-0549-3
  8. Chen H, Stasny EA, and Wolfe DA (2005). Ranked set sampling for efficient estimation of a population proportion, Statistics in Medicine, 24, 3319-3329. https://doi.org/10.1002/sim.2158
  9. Chen H, Stasny EA, and Wolfe DA (2006). Unbalanced ranked set sampling for estimating a population proportion, Biometrics, 62, 150-158. https://doi.org/10.1111/j.1541-0420.2005.00435.x
  10. Chen Z (2000). The efficiency of ranked-set sampling relative to simple random sampling under multi-parameter families, Statistica Sinica, 10, 247-263.
  11. Chen Z, Bai Z, and Sinha B (2004). Ranked Set Sampling: Theory and Application, Springer, New York.
  12. Deshpande JV (2013). Ranked set sampling for environmental studies, Retrieved March 1, 2016, from: http://www.samsi.info/sites/default/files/Deshpandemarch2013.pdf
  13. Jafari Jozani M, Majidi S, and Perron F (2012). Unbiased and almost unbiased ratio estimators of the population mean in ranked set sampling, Statistical Papers, 53, 719-737. https://doi.org/10.1007/s00362-011-0376-3
  14. Kadilar C, Unyazici Y, and Cingi H (2009). Ratio estimator for the population mean using ranked set sampling, Statistical Papers, 50, 301-309. https://doi.org/10.1007/s00362-007-0079-y
  15. Mahdizadeh M and Arghami NR (2012). Quantile estimation using ranked set samples from a population with known mean, Communications in Statistics - Simulation and Computation, 41, 1872-1881. https://doi.org/10.1080/03610918.2011.624236
  16. 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
  17. Murray RA, Ridout MS, and Cross JV (2000). The use of ranked set sampling in spray deposit assessment, Aspects of Applied Biology, 57, 141-146.
  18. Ozturk O and Deshpande JV (2006). Ranked-set sample nonparametric quantile confidence intervals, Journal of Statistical Planning and Inference, 136, 570-577. https://doi.org/10.1016/j.jspi.2004.07.011
  19. Samawi HM, Ahmed MS, and Abu-DayyehW(1996). Estimating the population mean using extreme ranked set sampling, Biometrical Journal, 38, 577-586. https://doi.org/10.1002/bimj.4710380506
  20. Samawi HM and Muttlak HA (1996). Estimation of ratio using rank set sampling, Biometrical Journal, 38, 753-764. https://doi.org/10.1002/bimj.4710380616
  21. 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
  22. Wolfe DA (2004). Ranked set sampling: an approach to more efficient data collection, Statistical Science, 19, 636-643. https://doi.org/10.1214/088342304000000369