Estimating a function from ergodic samples with additive noise

Author

Nobel, Andrew B. ; Adams, Terrence M.

Author_Institution

Dept. of Stat., North Carolina Univ., Chapel Hill, NC, USA

Volume

47

Issue

7

fYear

2001

fDate

11/1/2001 12:00:00 AM

Firstpage

2895

Lastpage

2902

Abstract

We study the problem of estimating an unknown function from ergodic samples corrupted by additive noise. It is shown that one can consistently recover an unknown measurable function in this setting, if the one-dimensional (1-D) distribution of the samples is comparable to a known reference distribution, and the noise is independent of the samples and has known mixing rates. The estimates are applied to deterministic sampling schemes, in which successive samples are obtained by repeatedly applying a fixed map to a given initial vector, and it is then shown how the estimates can be used to reconstruct an ergodic transformation from one of its trajectories

Keywords

function evaluation; noise; parameter estimation; signal reconstruction; signal sampling; 1D distribution; additive noise; deterministic sampling schemes; ergodic samples; ergodic transformation reconstruction; function estimation; initial vector; measurable function recovery; mixing rates; noise variance; reference distribution; Additive noise; Density measurement; Helium; Mathematics; Noise measurement; Sampling methods; Signal processing; Signal sampling; Statistical distributions; Trajectory;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.959268

Filename

959268