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On fractal distribution function estimation and applications


Theoretical background for affine IFS

2.1 Minimization approach

Theorem 1

Theorem 2 (Collage theorem)

Theorem 3 (Forte and Vrscay, 1995)

2.2 Direct approach

Theorem 4 (Iacus and La Torre, 2001).

Theorem 5 (Iacus and La Torre, 2001)

Corollary 6

Theorem 7

2.3 The choice of affine maps

3 Fourier analysis results

Theorem 8 (Forte and Vrscay, 1998)

Theorem 9 (Collage Theorem for FT, (Forte and Vrscay, 1998))

4 Statistical applications

4.1 Asymptotic results for the quantile-based IFS estimator

Theorem 10

Theorem 11

Theorem 12 (Gill and Levit, 1995)

Theorem 13

4.2 Characteristic function and Fourier density estimation

5 Monte Carlo analysis

5.1 Applications to survival analysis

Final remarks


On fractal distribution function estimation and applications


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[12] Golubev, G. K. and Levit, B. Y., "Asymptotic efficient estimation for analytic distributions", Math. Methods. Statist., 5, 357-368, 1996b.

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[14] Iacus, S.M. and La Torre, D., "Approximating distribution functions by iterated function systems", submitted, available as Acrobat PDF file at, 2001.

[15] Ihaka, R. and Gentleman, R., "R: A Language for Data Analysis and Graphics", Journal of Computational and Graphical Statistics, 5, 299-314, 1996.

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[19] Tarter, M.E. and Lock, M.D, Model free curve estimation, Chapman & Hall, New York, 1993.

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Stefano M. Iacus, Davide La Torre

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