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Abstrakty
The notion of conformal measures or densities goes back to Patterson’s work [8]. By a theorem of Milnor and Thurston [7] a piecewise monotone and continuous map of the interval is semiconjugate to one with constant slopes. The semiconjugacies can be defined by distribution functions of conformal measures as shown in [2]. In this note we show that for some transformations the conjugacies are estimable functions and can be used to improve estimation procedures, in particular density estimations.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
161--174
Opis fizyczny
Bibliogr. 12 poz., tab., wykr.
Twórcy
autor
- Mathematics Department, Pennsylvania State University, McAllister Building, State College, PA 16802, USA
autor
- Management, Marketing and Logistics, Boler School of Business, #209, John Carroll University, University Heights, OH 44118, USA
Bibliografia
- [1] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Math. Vol. 470, Springer, 1975.
- [2] M. Denker and M. Stadlbauer, Semiconjugacies for skew products of interval maps, in: Dynamics of Complex Systems, RIMS Kokyuroku 1404 (2004), pp. 12-20.
- [3] M. Denker and M. Urbański, On the existence of conformal measures, Trans. Amer. Math. Soc. 328 (1991), pp. 563-587.
- [4] S. Efromovich, Nonparametric Curve Estimation, Springer, New York 1999.
- [5] J. J. Faraway, Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, Chapman & Hall, Boca Raton-London-New York 2006.
- [6] S. Galatolo, M. Hoyrup and C. Rojas, A constructive Borel-Cantelli lemma. Constructing orbits with required statistical properties, Theoret. Comput. Sci. 410 (2009), pp. 2207-2222.
- [7] J. Milnor and W. Thurston, On iterated maps of the interval, in: Dynamical Systems (Maryland 1986-1987), Lecture Notes in Math. Vol. 1342, Springer, 1988, pp. 465-563.
- [8] S. J. Patterson, The limit set of a Fuchsian group, Acta Math. 136 (1976), pp. 241-273.
- [9] V. A. Rokhlin, On the fundamental ideas of measure theory, Mat. Sb. 25 (1949), pp. 107-150. Translation: Amer. Math. Soc. Transl. 71 (1952), pp. 1-54.
- [10] M. Stadlbauer, On random topological Markov chains with big images and preimages, Stochastics & Dynamics 10 (2010), pp. 77-95.
- [11] D. Sullivan, Conformal dynamical systems, in: Geometric Dynamics, Lecture Notes in Math. Vol. 1007, Springer, 1983, pp. 725-752.
- [12] L. Waterman, All of Nonparametric Statistics, Springer, New York 2006.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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