New estimators for the population median in simple random sampling
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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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Outline
Outline SAMPLING

  • 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
Introduction SAMPLING

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


Median estimators i n srs
Median Estimators SAMPLINGin SRS

  • Gross (1980)


Median estimators i n srs1
Median Estimators SAMPLINGin SRS

  • Kuk and Mak (1989)


Median estimators i n srs2
Median Estimators SAMPLINGin SRS

  • Kuk and Mak (1989)


Median estimators i n srs3
Median Estimators SAMPLINGin SRS

  • Singh, Singh and Puertas (2003)


Suggested median estimators
Suggested Median Estimators SAMPLING

  • Proposed 1


Suggested median estimators1
Suggested Median Estimators SAMPLING

  • Proposed 1


Suggested median estimators2
Suggested Median Estimators SAMPLING

  • Proposed 2


Suggested median estimators3
Suggested Median Estimators SAMPLING

  • Proposed 2


Suggested median estimators4
Suggested Median Estimators SAMPLING

  • Proposed 2


Suggested median estimators5
Suggested Median Estimators SAMPLING

  • Proposed 3


Suggested median estimators6
Suggested Median Estimators SAMPLING

  • Proposed 3


Suggested median estimators7
Suggested Median Estimators SAMPLING

  • A Family of Estimators


Suggested median estimators8
Suggested Median Estimators SAMPLING

  • A Family of Estimators



Efficiency comparisons1
Efficiency SAMPLING Comparisons



Numerical comparison s
Numerical Comparison SAMPLINGs

  • Data sets and statistics



Mean square errors of the estimators
Mean Square Errors of the SAMPLINGEstimators


Conclusion
Conclusion SAMPLING

  • 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
References SAMPLING

  • 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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