NEW ESTIMATORS FOR THE
POPULATION MEDIAN IN
SIMPLE RANDOM SAMPLING
Sibel Al
Hulya Cingi
Hacettepe University,
Hacettepe University,
Department of Statistics,
Department of Statistics,
Ankara, Turkey
Ankara, Turkey
Email:[email protected] Email:[email protected]
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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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References
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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
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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 auxiliary information.
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.
NEW ESTIMATORS FOR THE
POPULATION MEDIAN IN
SIMPLE RANDOM SAMPLING
Sibel Al
Hulya Cingi
Hacettepe University,
Hacettepe University,
Department of Statistics,
Department of Statistics,
Ankara, Turkey
Ankara, Turkey
Email:[email protected] Email:[email protected]