Annals of Statistics

Densities, spectral densities and modality

P. Laurie Davies and Arne Kovac

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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

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

First available in Project Euclid: 24 May 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Density estimation time series analysis spectral densities modality asymptotics strings


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

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