Densities, spectral densities and modality

Details Densities, spectral densities and modality Densities, spectral densities and modality

2004-10-05

arxiv.org/abs/math/0410071v1

Annals of Statistics 2004, Vol. 32, No. 3, 1093-1136

Mathematics

Statistics Theory

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat

Scientific paper

10.1214/009053604000000364

This paper considers the problem of specifying a simple approximating density function for a given data set (x_1,...,x_n). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The taut string method is used to control the numbers of modes and to produce candidate approximating densities. Refinements are introduced that improve the local adaptivity of the procedures and the method is extended to spectral densities.

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