The Annals of Probability

On density estimation from ergodic processes

Terrence M. Adams and Andrew B. Nobel

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Abstract

We consider the problem of $L_p$-consistent density estimation from the initial segments of strongly dependent processes. It is shown that no procedure can consistently estimate the one-dimensional marginal density of every stationary ergodic process for which such a density exists. A similar result is established for the problem of estimating the support of the marginal distribution of an ergodic process.

Article information

Source
Ann. Probab., Volume 26, Number 2 (1998), 794-804.

Dates
First available in Project Euclid: 31 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022855650

Digital Object Identifier
doi:10.1214/aop/1022855650

Mathematical Reviews number (MathSciNet)
MR1626511

Zentralblatt MATH identifier
0932.62042

Subjects
Primary: 62G07: Density estimation 60G17: Sample path properties 60G10: Stationary processes

Keywords
Density estimation ergodic processes cutting and stacking counter-example

Citation

Adams, Terrence M.; Nobel, Andrew B. On density estimation from ergodic processes. Ann. Probab. 26 (1998), no. 2, 794--804. doi:10.1214/aop/1022855650. https://projecteuclid.org/euclid.aop/1022855650


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