RATIO ESTIMATORS IN POST-STRATIFICATION

Öz

In this study, some ratio-type estimators are taken into consideration in literature and their properties are studied in post-stratification. Mean square error (MSE) of all ratio estimators in post-stratification is obtained and compared with the MSE of classical estimators in stratified random sampling. Within the frame work of the data from 2000 General Population size Census of Turkey which was carried out by the Turkish Statistical Institute (TURKSTAT), average employment has been estimated, and the population is taken as auxiliary variable by NUTS-1 Level. An application is carried out to show the superiority of the suggested ratio-estimators in post-stratification under the guidance of Turkey 2000 Population Census data.

SONRADAN TABAKALAMADA ORANSAL TAHMİN EDİCİLER

Öz

Bu çalışmada, literatürde verilen oransal tahmin edicilerin sonradan tabakalama yönteminde kullanımı incelenmiştir. Hata kareler ortalaması (HKO) elde edilmiş ve tabakalı rasgele örneklemede verilen oransal tahmin edicilerin HKO ile karşılaştırılmıştır. Türkiye İstatistik Kurumu tarafından gerçekleştirilen 2000 Türkiye Genel Nüfus Sayımı sonuçlarından idari birim bazında istihdam ve nüfus değerleri kullanılarak İstatistiki Bölge Birimleri Sınıflaması Düzey-1 bazında ortalama istihdam tahmin edilmiştir. Uygulama sonuçlarına göre sonradan tabakalama için önerilen oransal tahmin edicilerin daha iyi sonuç verdiği gösterilmiştir.

Kaynakça

1. Aksu, E.E., (2009). Post-stratification and an application. TURKSTAT Expertness thesis. Bacanli, S., Kadilar, C. (2008). “Ratio estimators with unequal probability designs”, Pakistan Journal of statistics, 24(3), 167-172.
2. Bethlehem, J. G. and Keller, W.J. (1987). “Linear Weighting of Sample Survey Data”, Journal Of Official Statistics 3(2), 141-153.
3. Cervantes, I.F. and Brick, J.F. (2009). “Efficacy of Poststratification in Complex Sample Design”, Proceedings of the Survey Research Methods Section, Alexandria, VA: American Statistical Association. 4642-4655.
4. Cochran, W.G. (1977). Sampling Techniques. New York; Wiley.
5. Hansen, M.H., Hurwitz, W.N., Madow W.G. (1953). Sample Survey Methods and Theory Volume II-Theory. Canada; John Wiley&Sons, Incorporation.
6. Holt, D., Smith, T.M.F.(1979). “Post-Stratification” , Journal of the Royal Statistical Society A, 142, 46.
7. Kadilar, C., Cingi, H. (2003). “Ratio estimators in stratified random sampling”, Biometrical Journal. (2003)2, 218-225.
8. Kim, J.J., Li, J., and Valliant, R. (2007). “Cell Collapsing in Poststratification”, Survey Methodology, , 139-150.

9. Rueda, M. M., Gonzalez, S. and Arcos, A. (2006). “A general class of estimators with auxiliary information based on available units”, Applied Mathematics and computation. 175, 131-148.
10. Särndal, C.E., Swensson, B., Wretman, J. (2003). Model Assisted Survey Sampling. New York; Springer.
11. Singh, S. (2003). Advanced sampling theory with applications. Kluwer, Netherlands
12. Sisodia, B. V. S. and Dwivedi, V. K.. (1981). “A Modified ratio estimator using coefficient of variation of auxiliary variable”, Journal of Indian Society Agricultural Statistics. 33, 13–18.
13. Upadhyaya, L. N. and Singh, H. P., (1999). “Use of transformed auxiliary variable in estimating the finite population mean”, Biometrical Journal 41, 5, 627–636.
14. Zhang, Li-Chun (2000). “ Post-Stratification and Calibration- A Synthesis”, The American Statistician, 54, 178-184.