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April 1998 On density estimation from ergodic processes
Terrence M. Adams, Andrew B. Nobel
Ann. Probab. 26(2): 794-804 (April 1998). DOI: 10.1214/aop/1022855650


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.


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Terrence M. Adams. Andrew B. Nobel. "On density estimation from ergodic processes." Ann. Probab. 26 (2) 794 - 804, April 1998.


Published: April 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0932.62042
MathSciNet: MR1626511
Digital Object Identifier: 10.1214/aop/1022855650

Primary: 60G10 , 60G17 , 62G07

Keywords: counter-example , cutting and stacking , Density estimation , Ergodic processes

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 2 • April 1998
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