JSM 2005 Online Program

Abstract #302382

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Activity Number:	205
Type:	Invited
Date/Time:	Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
Sponsor:	IMS
Abstract - #302382
Title:	Another Shape Constraint and Multiscale Methods for Density Estimation
Author(s):	Lutz Duembgen*+
Companies:	University of Bern
Address:	Department of Statistics, Bern, International, CH-3012, Switzerland
Keywords:	log-concavity ; multiscale testing ; distribution-free ; density estimation ; adaptivity
Abstract:	In nonparametric curve estimation, shape constraints such as monotonicity or convexity are known to yield estimators adapting to unknown smoothness properties of the underlying curve. This talk discusses a particular shape constraint in the context of density estimation. We assume the underlying density is log-concave and show that the resulting nonparametric estimators of the density and distribution function have various interesting properties. While log-concavity is a reasonable assumption in connection with homogeneous populations, another task in density estimation is inference about modality and local log-concavity or -convexity. We present some multiscale procedures for these purposes, yielding confidence statements with guaranteed level for finite samples. This is joint work with Kaspar Rufibach (Bern) and Guenther Walther (Stanford).

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