Kernel density estimation via diffusion and the complex exponentials approximation problem

Author:
Piero Barone

Journal:
Quart. Appl. Math. **72** (2014), 291-310

MSC (2010):
Primary 62G07, 41A30

Published electronically:
February 5, 2014

MathSciNet review:
3186238

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when the complex exponentials approximation problem is considered in Gaussian noise. Several moments problems can be formulated in this framework, and the estimation of the condensed density above is the main critical step for their solution. It is shown that the condensed density satisfies approximately a diffusion equation, which allows us to estimate an optimal bandwidth. It is proved by simulation that good results can be obtained even when the signal-to-noise ratio is so small that other methods fail.

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Additional Information

**Piero Barone**

Affiliation:
Istituto per le Applicazioni del Calcolo “M. Picone”, C.N.R., Via dei Taurini 19, 00185 Rome, Italy

Email:
p.barone@iac.cnr.it, piero.barone@gmail.com

DOI:
https://doi.org/10.1090/S0033-569X-2014-01333-4

Keywords:
Condensed density,
random matrices,
parabolic PDE

Received by editor(s):
June 20, 2012

Published electronically:
February 5, 2014

Article copyright:
© Copyright 2014
Brown University

The copyright for this article reverts to public domain 28 years after publication.