The Annals of Statistics

Densities, spectral densities and modality

P. Laurie Davies and Arne Kovac

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Abstract

This paper considers the problem of specifying a simple approximating density function for a given data set (x1,…,xn). 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.

Article information

Source
Ann. Statist., Volume 32, Number 3 (2004), 1093-1136.

Dates
First available in Project Euclid: 24 May 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1085408496

Digital Object Identifier
doi:10.1214/009053604000000364

Mathematical Reviews number (MathSciNet)
MR2065199

Zentralblatt MATH identifier
1093.62042

Subjects
Primary: 62G07: Density estimation
Secondary: 62M15: Spectral analysis

Keywords
Density estimation time series analysis spectral densities modality asymptotics strings

Citation

Davies, P. Laurie; Kovac, Arne. Densities, spectral densities and modality. Ann. Statist. 32 (2004), no. 3, 1093--1136. doi:10.1214/009053604000000364. https://projecteuclid.org/euclid.aos/1085408496


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