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Conformal measures and density estimation

Denker M., Facca T.

Probability and Mathematical Statistics

2011

Vol. 31, Fasc. 1

161--174

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.