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NEW ESTIMATORS FOR THE POPULATION MEDIAN IN SIMPLE RANDOM SAMPLING

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NEW ESTIMATORS FOR THE POPULATION MEDIAN IN SIMPLE RANDOM SAMPLING

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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

Introduction

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

Median Estimators in SRS

- Gross (1980)

Median Estimators in SRS

- Kuk and Mak (1989)

Median Estimators in SRS

- Kuk and Mak (1989)

Median Estimators in SRS

- Singh, Singh and Puertas (2003)

Suggested Median Estimators

- Proposed 1

Suggested Median Estimators

- Proposed 1

Suggested Median Estimators

- Proposed 2

Suggested Median Estimators

- Proposed 2

Suggested Median Estimators

- Proposed 2

Suggested Median Estimators

- Proposed 3

Suggested Median Estimators

- Proposed 3

Suggested Median Estimators

- A Family of Estimators

Suggested Median Estimators

- A Family of Estimators

Numerical Comparisons

- Data sets and statistics

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.

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.

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