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NEW ESTIMATORS FOR THE POPULATION MEDIAN IN SIMPLE RANDOM SAMPLING

NEW ESTIMATORS FOR THE POPULATION MEDIAN IN SIMPLE RANDOM SAMPLING. Outline. Introduction Median estimators in SRS Gross (1980) Kuk and Mak (1989) Singh, Singh and Puertas (2003) Suggested median estimators Proposed 1 Proposed 2 Proposed 3 A family of estimators

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NEW ESTIMATORS FOR THE POPULATION MEDIAN IN SIMPLE RANDOM SAMPLING

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  1. NEW ESTIMATORS FOR THE POPULATION MEDIAN IN SIMPLE RANDOM SAMPLING

  2. Outline • Introduction • Median estimators in SRS • Gross (1980) • Kuk and Mak (1989) • Singh, Singh and Puertas(2003) • Suggested median estimators • Proposed 1 • Proposed 2 • Proposed 3 • A family of estimators • Efficiency comparisons • Numerical comparisons • Conclusion

  3. Introduction • Median is a measure which divides the population into exactly two equal parts and it is denoted by MY .

  4. Median Estimators in SRS • Gross (1980)

  5. Median Estimators in SRS • Kuk and Mak (1989)

  6. Median Estimators in SRS • Kuk and Mak (1989)

  7. Median Estimators in SRS • Singh, Singh and Puertas (2003)

  8. Suggested Median Estimators • Proposed 1

  9. Suggested Median Estimators • Proposed 1

  10. Suggested Median Estimators • Proposed 2

  11. Suggested Median Estimators • Proposed 2

  12. Suggested Median Estimators • Proposed 2

  13. Suggested Median Estimators • Proposed 3

  14. Suggested Median Estimators • Proposed 3

  15. Suggested Median Estimators • A Family of Estimators

  16. Suggested Median Estimators • A Family of Estimators

  17. Efficiency Comparisons

  18. Efficiency Comparisons

  19. Efficiency Comparisons

  20. Numerical Comparisons • Data sets and statistics

  21. Members of the proposed family of estimators

  22. Mean Square Errors of theEstimators

  23. Conclusion • We suggest new median estimators using a known constant. • We theoretically show that these estimators are always more efficient than classical estimators. • In the numerical examples, the theoretical results are also supported. • In future works, we hope to adapt the estimators proposed in this study to stratified random sampling.

  24. References • Chen, Z., Bai, Z., Sinha, B.K. (2004). Ranked Set Sampling Theory and Applications. New York: Springer-Verlag. • Cingi, H., Kadilar, C., Kocberber, G. (2007). Examination of educational opportunities at primary and secondary schools in Turkey suggestions to determined issues. TUBITAK, SOBAG, 106K077. http://yunus.hacettepe.edu.tr/~hcingi/ • Gross, T.S. (1980). Median estimation in sample surveys. Proc. Surv. Res. Meth. Sect. Amer. Statist. Ass. 181-184. • Kuk, A.Y.C., Mak, T.K. (1989). Median estimation in the presence of auxiliaryinformation. Journal of the Royal Statistical Society Series, B, 51, 261-269. • Prasad, B. (1989). Some improved ratio type estimators of population mean and ratio in finite population sample surveys. Communications in Statistics Theory Methods, 18, 379-392. • Searls, D.T. (1964). The utilization of a known coefficient of variation in the estimation procedure. Journal of the American Statistical Association, 59, 1225–1226. • Singh, S. (2003). Advanced Sampling Theory with Applications: How Michael ‘selected’ Amy. London: Kluwer Academic Publishers. • Singh, H.P., Singh, S., Joarder, A.H. (2003a). Estimation of population median when mode of an auxiliary variable is known. Journal of Statistical Research, 37, 1, 57-63. • Singh, H.P., Singh, S., Puertas, S.M. (2003b). Ratio type estimators for the median of finite populations. Allgemeines Statistisches Archiv, 87, 369-382.

  25. NEW ESTIMATORS FOR THE POPULATION MEDIAN IN SIMPLE RANDOM SAMPLING

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