new estimators for the population median in simple random sampling sibel al hacettepe university,...
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NEW ESTIMATORS FOR THE POPULATION MEDIAN IN
SIMPLE RANDOM SAMPLING
Sibel AlHacettepe University,
Department of Statistics, Ankara, Turkey
Email:[email protected]
Hulya CingiHacettepe University,
Department of Statistics, Ankara, Turkey
Email:[email protected]
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
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Introduction• Median is a measure which divides the population into exactly two
equal parts and it is denoted by MY .
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Median Estimators in SRS
•Gross (1980)
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Median Estimators in SRS•Kuk and Mak (1989)
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Median Estimators in SRS•Kuk and Mak (1989)
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Median Estimators in SRS
•Singh, Singh and Puertas (2003)
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Suggested Median Estimators•Proposed 1
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Suggested Median Estimators•Proposed 1
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Suggested Median Estimators•Proposed 2
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Suggested Median Estimators•Proposed 2
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Suggested Median Estimators•Proposed 2
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Suggested Median Estimators•Proposed 3
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Suggested Median Estimators•Proposed 3
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Suggested Median Estimators•A Family of Estimators
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Suggested Median Estimators•A Family of Estimators
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Efficiency Comparisons
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Efficiency Comparisons
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Efficiency Comparisons
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Numerical Comparisons•Data sets and statistics
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Members of the proposed family of estimators
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Mean Square Errors of the Estimators
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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.
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References1. Chen, Z., Bai, Z., Sinha, B.K. (2004). Ranked Set Sampling Theory and Applications. New
York: Springer-Verlag.
2. 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/
3. Gross, T.S. (1980). Median estimation in sample surveys. Proc. Surv. Res. Meth. Sect. Amer. Statist. Ass. 181-184.
4. Kuk, A.Y.C., Mak, T.K. (1989). Median estimation in the presence of auxiliary information. Journal of the Royal Statistical Society Series, B, 51, 261-269.
5. 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.
6. 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.
7. Singh, S. (2003). Advanced Sampling Theory with Applications: How Michael ‘selected’ Amy. London: Kluwer Academic Publishers.
8. 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.
9. Singh, H.P., Singh, S., Puertas, S.M. (2003b). Ratio type estimators for the median of finite populations. Allgemeines Statistisches Archiv, 87, 369-382.
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NEW ESTIMATORS FOR THE POPULATION MEDIAN IN
SIMPLE RANDOM SAMPLING
Sibel AlHacettepe University,
Department of Statistics, Ankara, Turkey
Email:[email protected]
Hulya CingiHacettepe University,
Department of Statistics, Ankara, Turkey
Email:[email protected]