Conformal measures and density estimation

Manfred Heinz Denker, Tina Facca

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)161-174
Number of pages14
JournalProbability and Mathematical Statistics
Volume31
Issue number1
StatePublished - Aug 1 2011

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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