Karmaşık Örnekleme Planlarında Çeşitli Varyans Tahmin Yöntemleri ve Uygulama

Öz

Bu çalışmada karmaşık örnekleme planlarında varyans tahmini için kullanılan yöntemler incelendi. İlk bölümde konuya giriş yapıldı. İkinci bölümde karmaşık örnekleme planlarında varyans tahmin yöntemlerinden olan Taylor serisi yöntemi, üçüncü bölümde rasgele grup yöntemlerinden bağımlı rasgele grup ile bağımsız rasgele grup yöntemleri, dördüncü bölümde tekrarlı yöntemlerden dengeli olarak tekrarlanan tekrarlı yöntem, jacknife yöntemi ve bootstrap yöntemi, beşinci bölümde ise genelleştirilmiş varyans fonksiyonu incelenerek kuramsal özellikleri, yöntemlerin uygulanış şekilleri, örneklem planındaki kısıtlamaları üzerinde duruldu. Altıncı bölümde açıklanan yöntemler kuramsal özellikleri, uygulanış şekilleri, sonuçlardaki doğruluk ve maliyetleri bakımından karşılaştırıldı. Yedinci bölümde ise bugüne dek karmaşık örnekleme planlarında varyans eşitlikleri incelenmemiş olan oransal, çarpımsal, regresyon tahmin edicileri için açıklanan yöntemler kullanılarak elde edilen varyans eşitlikleri verildi. Sekizinci bölümde açıklanan yöntemleri kullanarak Ankara ilinde bulunan 843 sanayi kuruluşundan tabakalı sistematik örnekleme ile elde edilen 163 birimlik örneklemden bazı özelliklerin tahminleri ve varyans tahminlerini elde etmek amacıyla yazılmış programdan elde edilen sonuçlardan bazı örnekler verildi ve elde edilen bu sonuçlar ile yöntemler karşılaştırıldı.

Anahtar Kelimeler

• Varyans Tahmini
• Karmaşık Örneklemler
• Yeniden (Tekrarlı) Örnekleme Yöntemleri

Various Variance Estimation Methods for Complex Sampling Survey and Application

Öz

In this study, variance estimation methods for complex sampling survey were examined. In the first chapter a brief introduction was made. In the following chapters, Taylor series method, dependent and independent random group methods from random group method, balanced repeated replication method, jackknife and bootstrap methods from resampling methods and lastly generalized variance function were examined, theoretical properties, methods appliance forms, restrictions of sampling were studied. In the sixth chapter, these methods were compared with each other based on their theoretical properties, appliance forms, accuracy of results and costs. In the seventh chapter, variance equations were obtained using the methods those are described for ratio, multiplier and regression estimators whose variance equations have not been examined in complex sampling survey up to now. In the eigth chapter, some results obtained from a software application developed to obtain estimators and variance equations over a stratified systematic sampling having 163 units, obtained from 843 industrial corporations in Ankara were given. Lastly some results of estimators and variance estimators which were obtained from these methods were placed and compared with each other.

Anahtar Kelimeler

• Variance Estimation
• Complex Survey
• Resampling Methods

Kaynakça

1. CHAO, M. and LO, S. (1985), A Bootstrap Methods for Finite Population, the Indian Journal of Statistics, 47, Series A, 399-405.
2. CHERNICK, M.R. (1999), Bootstrap Methods a Practitioner’s Guide: John Wiley & Sons.
3. COHEN, S.B. (1997), an Evulation of Alternative PC-Based Software Packages Developed for the Analysis of Complex Survey Data, the American Statistician, 51, No.3, 285-292.
4. EFRON, B. (1979), Bootstrap Methods Another Look At The Jacknife, the Annals of Statistics, 7, No.1, 1-26.
5. EFRON, B. and TİBSHIRANI, R.J. (1993), an Introduction to the Bootstrap: Chapman&Hall International Thompson Publishing.
6. HEDAYET, A. S. and SINHA, B.K. (1991), Design and Inference in Finite Population Sampling, a Wiley-Interscience Publication, New York: John Wiley &Sons.
7. KİSH, L. and FRANKEL., M.R.(1974), Inference from Complex Samples, Journal of Royal Statistical Society, B(36), 1-37.
8. KİSH, L. and FRANKEL, M.R. (1970), Balanced Repeated Replications for Standard Errors, Journal of American Statistical Association, 65, 1071-1095.

9. LEE, K.H. (1972), Partially Balanced Designs for Half Sample Replication Method of Variance Estimation, Journal of American Statisticial Association, 67, No.338, 324-334.
10. LEPLOWSKİ, J. and BOWLES, J. (1996), Sampling Error Software for Personel Computers, the Survey Statistician, 35, 10-17.
11. LOHR, S.L. (1999), Sampling: Design and Analysis: Duxbury Press.
12. MİLLER, R.G. (1974), the Jacknife a Review, Biometrika, 61, 1-15.
13. RAJ, D. (1998), Sample Survey Theory, Naraso Publishing House: London.
14. RAO, J.N.K. (1997), Developmnets in Sample Survey Theory: an Apprasial, the Canadian Journal of Statistics, 25, 1-21.
15. RAO, J.N.K. and KREWSKİ, D. (1981), Inference from Stratified Samples; Properties of the Linearization, Jacknife and Balanced Repeated Replication Methods, the Annals of Statistics, 9, No. 5, 1010-1019.
16. RAO, J.N.K. and WU, C.F.J. (1988), Resampling Inference with Complex Survey Data, Journal of American Statisticial Association, 83, No.401, 231-241.
17. RAO, J.N.K. and WU, C.F.J. (1985), Inference from Stratified Samples: Second-Order Analysis of Three Methods for Nonlinear Statistics, Journal of American Statisticial Association, 80, No.391, 620-630.
18. SARNDAL, C.E., SWENSON B. and WRETMAN J. (1991), Model Assisted Survey Sampling, New York,: Springer Series-Verlag,.
19. TOPRAK, A.Ö. (1996), Karmaşık Örnekleme Planlarında Varyans Tahmini, Bilim Uzmanlığı Tezi, Orta Doğu Teknik Üniversitesi.
20. VAILLANT, R. (1987), Generalized Variance Functions in Stratified Two-Stage Sampling, Journal of American Statisticial Association, 82, No.398, 499-508.
21. VERMA, V. (1992), Sampling Methods, Statisticial Institute for Asia and the Pacific, Tokyo.
22. WODDRUFF, R. S. (1971), a Simple Method for Approximating the Variance of a Comlicated Estimate, Journal of American Statisticial Association, 66, 411-414.
23. WOODRUFF, R.S. and CAUSEY, B. D. (1976), Computerized Method for Approximating the Variance of a Complicated Estimate, Journal of American Statisticial Association, 71, No.354, 315-321.
24. WOLTER, K.M. (1985), Introduction to the Variance Estimation, Springer Series in Statistics, New York.