Dağılım fonksiyonlarının yinelenmis fonksiyon sistemleri ile tahmini

Öz

Bir dağılım fonksiyonunun parametrik olmayan tahmin edicisi yinelenmis fonksiyon sistemleri kullanılarak

elde edilebilmektedir. Bu yönteme göre, bir dağılım fonksiyonunun tahmin edicisi, (X1, X2,…,Xn)

örneklemine bağlı olan bir p parametre vektörü ve w afin dönüsümleri ailesine göre tanımlanan T daralma

operatörünün bir sabit noktası olarak düsünülmektedir. Döviz kuru verisi üzerinde yapılan uygulamadan elde

edilen sonuçlar bir örnek olarak gösterilmistir.

Anahtar Kelimeler

• Fraktallar,yinelenmis fonksiyon sistemleri,dağılım fonksiyonu,parametrik olmayan tahmin,yoğunluk tahmini

Estimating the distribution functions by iterated function system

Öz

A class of nonparametric estimators of a distribution function base on the theory of iterated function systems

(IFS). The estimator is considered as the fixed point of a contractive operator T defined in terms of a vector of

parameters p and a family of affine maps which can be both depend on the sample (X1, X2,…,Xn). An

application to exchange data is showed as an example.

Anahtar Kelimeler

• Fractals,iterated function systems,distribution function estimation,nonparametric estimation,density estimation.

Kaynakça

1. Maldrbrot, B. (1982) The Fractal Geometry of Nature, W.H. Freeman and Co., San Francisco.
2. Barnsley, M. F. (1993), Fraktals Everywhere, Academic Press.
3. Barnsley, M. F. and Demko, S. (1985), Iterated function systems and the global construction of fractals, Proc. Roy. Soc. London, Ser A, 399, 243-275.
4. Devaney, R, L.(1993), A First Course in Chaotic Dynamical Systems, Persaus Books Pub.
5. Forte, B. and Vrscay, E.R. (1994), Solving the inverse problem for function/image approximation using iterated function systems, I. Theoretical basis, Fractal, 2, 3, 325-334.
6. S.M. Iacus and D. La Torre., “Approximating distribution functions by iteration functions systems and applications”, Proceedings the S.I.M.A.I. Confarence, Chia Laguna, Italy, 2002.
7. S.M. Iacus and D. La Torre (2002), Fractals and Statistics: an R package 'Distributed Statistical Computing' (DSC 2003). D. La Torre (2002), On fractals distribution function estimation and applications,partemental Working Papers 2002-07, Dep. of Economics, University
8. S.M. Iacus and D. La Torre (2002), On fractals distribution function estimation and applications, Departemental Working Papers 2002-07, Dep. of Economics, University of Milan, Italy.

9. S.M. Iacus and D. La Torre (2002), Nonparametric estimation of distribution and density function in presence missing data: an IFS approach, Departemental Working Papers 2002-25, Dep. of Economics, University of Milan, Italy.
10. S.M. Iacus and D. La Torre (2005), Approximating distribution functions by iterated function systems, J.Appl.Math. Dec.Sci., 1, 334-345.
11. S.M. Iacus and D. La Torre (2005), A comparative simulation study on the IFS distribution function estimator, Nonlinear Analysis: Real World Applications, 6, 774-785.