Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Estimation of Median in the Presence of Three Known Quartiles of an Auxiliary Variable

  • Singh, Housila P. (School of Studies in Statistics, Vikram University) ;
  • Shanmugam, Ramalingam (School of Health Administration, Texas State University) ;
  • Singh, Sarjinder (Department of Mathematics, Texas A&M University-Kingsville) ;
  • Kim, Jong-Min (Statistics Discipline, University of Minnesota at Morris)
  • Received : 2013.10.17
  • Accepted : 2014.09.04
  • Published : 2014.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper has improved several ratio type estimators of the population median including their generalization in the presence of three known quartiles of an auxiliary variable. The properties of the improved estimators are discussed and applied. Both the empirical and simulation studies confirm that our new estimators perform efficiently.

Keywords

References

  1. Allen, J., Singh, H. P., Singh, S. and Smarandache, F. (2002). A General Class of Estimators of Population Median Using Two Auxiliary Variables in Double Sampling, In Randomness and Optimal Estimation in Data Sampling, Amer. Res. Press, Rehoboth, New Mexico, USA 26-43.
  2. Arcos, A., Rueda, M. and Martinez-Miranda, M. D. (2005). Using multiparametric auxiliary information at the estimation stage, Statistical Papers, 46, 339-358. https://doi.org/10.1007/BF02762838
  3. Chambers, R. L. and Dustan, R. (1986). Estimating distribution functions from survey data, Biometrika, 73, 597-604. https://doi.org/10.1093/biomet/73.3.597
  4. Cochran, W. G. (1963). Sampling Techniques, John Wiley and Sons, New York.
  5. Garcia, M. R. and Cebrian, A. A. (2001). On estimating the median from survey data using multiple auxiliary information, Metrika, 59-76.
  6. Gross, T. S. (1980). Median estimation in sample surveys, Proc. Surv. Res. Meth. Sect. Amer. Statist. Ass., 181-184.
  7. Kuk, A. Y. C. and Mak, T. K. (1989). Median estimation in the presence of auxiliary information, J. Roy. Statist. Soc., B, 51, 261-269.
  8. Mak, T. K. and Kuk, A. Y. C. (1993). A new method for estimating finite population quantiles using auxiliary information, Canadian J. Staist., 21, 29-38. https://doi.org/10.2307/3315655
  9. Meeden, G. (1995). Median estimation using auxiliary information, Survey Methodology, 21, 71-77.
  10. Meeden, G. and Vardeman, S. (1991). A noninformative Bayesian approach to interval estimation in finite population sampling, J. Amer. Statist. Assoc., 86, 972-980. https://doi.org/10.1080/01621459.1991.10475140
  11. Rao, J. N. K., Kovar, J. G. and Mantel, H. J. (1990). On estimating distribution functions and quantiles from survey data using auxiliary information, Biometrika, 77, 365-375. https://doi.org/10.1093/biomet/77.2.365
  12. Rueda, M. M., Arcos, A., Martinez-Miranda, M. D. and Roman, Y. (2004). Some improved estimators of finite population quantile using auxiliary information in sample surveys, Computational Statistics and Data Analysis, Elsevier, 45, 825-848. https://doi.org/10.1016/S0167-9473(03)00097-5
  13. Rueda, M. D. M. and Arcos, A. (2002). The use of quantiles of auxiliary variables to estimate medians, Biom. J., 44, 619-632. https://doi.org/10.1002/1521-4036(200207)44:5<619::AID-BIMJ619>3.0.CO;2-D
  14. Rueda, M., Arcos, A., Gonzalez-Aguilera, S., Martinez-Miranda, M. D., Roman, Y. and Martinez-Puertas, S. (2005). Ratio methods to the mean estimation with known quantiles, App. Math. Compu., 170, 1031-1044. https://doi.org/10.1016/j.amc.2005.01.008
  15. Sharma, P. And Singh, R. (2014). Generalized class of estimators for population median using auxiliary information, Hec. Journal of Math and Stat., In press.
  16. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis, Chapman & Hall, London.
  17. Singh, H. P., Chandra, P., Joarder, A. H. and Singh, S. (2007). Family of estimators of mean, ratio and product of a finite population using random non response, Test, 16, 565-597. https://doi.org/10.1007/s11749-006-0020-z
  18. Singh, H. P., Sidhu, S. S. and Singh, S. (2006). Median estimation with known interquartile range of auxiliary variable, Int. J. Appl. Math. Stat, March Issue, 68-80.
  19. Singh, H. P., Singh, S. and Puertas, S. P. (2006). Estimation of interquartile range of the study variable using the known interquartile range of auxiliary variable, Int. J. Appl. Math. Stat., 6, 33-47.
  20. Singh, H. P., Singh, S. and Puetas, S. M. (2003). Ratio type estimators for the median of finite populations, Allgemeines Statistiches Archiv., 369-382.
  21. Singh, H. P., Tailor, R., Singh, S. and Kim, J. M. (2007). Quartile estimation in successive sampling, Journal of the Korean Statistical Society, 36, 543-556.
  22. Singh, H. P. and Solanki, R. S. (2013). Some classes of estimators for the population median using auxiliary information, Communications in Statistics-Theory and Methods, 42, 4222-4238. https://doi.org/10.1080/03610926.2011.648794
  23. Singh, S., Joarder, A. H. and Tracy, D. S. (2001). Median estimation using double sampling, Aust. & New Zealand J. Statist., 43, 33-46. https://doi.org/10.1111/1467-842X.00153
  24. Singh, S. and Puertas, S. M. (2003). On the estimation of total, mean and distribution function using two-phase sampling: Calibration approach, Jour. Ind. Soc. Ag. Stat., 56, 237-252.
  25. Singh, S., Singh, H. P. and Upadhayaya, L. N. (2007). Chain ratio and regression type estimators for median estimation in survey sampling, Statistical Papers, 48, 23-46. https://doi.org/10.1007/s00362-006-0314-y
  26. Srivastava, S. K. and Jhajj, H. S. (1981). A class of estimators of the population mean in survey sampling using auxiliary information, Biometrika, 68, 341-343 https://doi.org/10.1093/biomet/68.1.341