KARŞILAŞTIRMALI OLARAK FONKSİYONEL ANA BİLEŞENLER ANALİZİ VE GSYİH VERİLERİNİN İNCELENMESİ

Öz

Bu çalışmada öncelikle Ana Bileşenler ve Fonksiyonel Ana Bileşenler Analizi karşılaştırmalı olarak ele alınmış ve ekonomik gelişmenin bir göstergesi olan Gayri Safi Yurt İçi Hasıla (GSYİH) verileri Fonksiyonel Ana Bileşenler Analizi ile incelenerek verileri fonksiyonel açıdan ele almanın avantajları sunulmuştur. Fonksiyonel Ana Bileşenler Analizi ile 1987-2001 yılları arasında ülkemizdeki 7 bölgenin GSYİH verilerinin değişkenlik yapısı %99 gibi çok yüksek bir varyans açıklama yüzdesine sahip birinci ana bileşen fonksiyonuyla ortaya konulmuştur. Bu ana bileşen fonksiyonun yardımıyla GSYİH açısından bölgeler arasındaki değişkenliğin 1996 yılından sonra bir artışa geçtiği, ancak 2000 yılının ortalarından sonra da tekrar azalmaya başladığı tespit edilmiştir

Anahtar Kelimeler

• Fonksiyonel Veri Analizi, Fonksiyonel Ana Bileşenler Analizi

FUNCTIONAL PRINCIPAL COMPONENT ANALYSIS: INVESTIGATION OF GDP DATA

Öz

In this study, Principal Components and Functional Principal Components Analyses discussed comparatively. Gross Domestic Product (GDP) data is analyzed by Functional Principal Component Analysis and the advantages of dealing data in a functional way is presented. GDP data (between 1987 and 2001) for seven regions of Turkey is studied by Functional Principal Component Analysis, it is found that %99 of the variation structure can be explained by the first principal component function. It is also revealed that the variation between regions began to increase after the year 1996. However, it began to decrease rapidly after year 2000

Anahtar Kelimeler

• Functional Data Analysis, Functional Principal Component Analysis

Kaynakça

1. ANDERSON T.W. (2003). “An Introduction to Multivariate Statistical
2. Analysis”,Wiley-Interscience, USA BARRA V. (2004). “Analysis of Gene Expression Data Using Functional
3. Principal Components”, Computer Methods and Programs in Biomedicine, (1):1-9. BENKO M. (2004). “Functional Principal Components analysis, Implementation and Applications”. A Master Thesis, Humboldt University Center of Applied
4. Statistics and Economics, Berlin. BENKO M., HARDLE W., and KNEİP A.(2006). “Common Functional Principal
5. Components” SFB 649, DiscussionPaper http://ideas.repec.org/p/hum/wpaper/sfb649dp2006-010.html, (10.11.2006)
6. CASTRO P. E, LAWTON W. H., and SYLVESTRE E. A. (1986). “Principal
7. Modes Of Variation for Processes with Continuous Sample Curves” ,Technometrics, 28(4 ):329-337. HALL P. and NASAB H. M. (2006). “On Properties Of Functional Principal
8. Components Analysis”, Journal of the Royal Statistical Society: Series B, (1):109-126. JAMES G. M., HASTİE T.J., and SUGAR C.A. (2000), “Principal Components

9. Models For Sparse Functional Data”, Biometrica, 87(3):587-602. JOLIFFE I.T. (2002). “Principal Component Analysis”,Springer – Verlag, New York.
10. LEE H.J. (2004). “Functional Data Analysis: Classification and Regression”.
11. Doctor of Philosophy, Texas A&M University. LOBER E.M., and VİLLA C. (2004). “Functional Principal Component Analysis of the Yield Curve”, http://www.u-cergy.fr/AFFI_2004/IMG/pdf/MATZNER.pdf, (05.05.2005).
12. LOBER E.M., and VİLLA C. (2004). “Functional Principal Component Analysis of the Yield Curve”, http://www.u-cergy.fr/AFFI_2004/IMG/pdf/MATZNER.pdf, (05.05.2005).
13. LYCHE, T. and MORKEN, K., (2002). “Spline Methods Draft”, http://www.ifi.uio.no/in329/nchap1.pdf ,( 10.07.2005).
14. MARDİA K.V., KENT J.T., and BİBBY J.M. (1989). “Multivariate Analysis”,
15. Academic Press, London. RAMSAY J.O., & SİLVERMAN B.W. (2005). “Functional Data Analysis” Second
16. Edition, Springer , USA. RAMSAY J.O., (2000). “Functional Principal Component Analysis”, , ftp://ego.psych.mcgill.ca, (11.04.2005).
17. RAMSAY J.O., and SİLVERMAN B.W. (1997). “Functional Data Analysis”,
18. Springer – Verlag, New York. RAMSAY, J. O., and DALZELL C. (1991). “Some Tools For Functional Data
19. Analysis”, Journal of the Royal Statistical Society: Series B.,53 (3):539-572. RAMSAYJ.O.,(2003).,http://www.psych.mcgill.ca/faculty/ramsay/ramsay.html, (11.04.2005).
20. TÜİK (2007), http://www.tuik.gov.tr, (14.08. 2007 ).
21. YAMANİSHİ Y., & TANAKA Y. (2005). “Sensitivity Analysis in Functional
22. Principal Component Analysis” Computational Statistics, 20(2):313-329.