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Quantitative L2 Approximation Error of a Probability Density Estimate Given by It Samples

T. Blu, M. Unser

Proceedings of the Twenty-Ninth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'04), Montréal QC, Canada, May 17-21, 2004, pp. III-952-III-955.


We present a new result characterized by an exact integral expression for the approximation error between a probability density and an integer shift invariant estimate obtained from its samples. Unlike the Parzen window estimate, this estimate avoids recomputing the complete probability density for each new sample: only a few coefficients are required making it practical for real-time applications.

We also show how to obtain the exact asymptotic behavior of the approximation error when the number of samples increases and provide the trade-off between the number of samples and the sampling step size.

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/blu0402.html,
AUTHOR="Blu, T. and Unser, M.",
TITLE="Quantitative ${\mathbf L}^{2}$ Approximation Error of a
	Probability Density Estimate Given by It Samples",
BOOKTITLE="Proceedings of the Twenty-Ninth {IEEE} International
	Conference on Acoustics, Speech, and Signal Processing
	({ICASSP'04})",
YEAR="2004",
editor="",
volume="{III}",
series="",
pages="952--955",
address="Montr{\'{e}}al QC, CA",
month="May 17-21,",
organization="",
publisher="",
note="")

© 2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
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