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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 31, Fasc. 1,
pages 161 - 174
 

CONFORMAL MEASURES AND DENSITY ESTIMATION

Manfred Denker
Tina Facca

Abstract: 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.

2000 AMS Mathematics Subject Classification: Primary: 62G05, 37E05; Secondary: 62G07, 62G09, 37A05, 37A50.

Keywords and phrases: Resampling, interval map, conjugacy, density estimation.

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