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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. 

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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})",
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volume="{III}",
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pages="952--955",
address="Montr{\'{e}}al QC, CA",
month="May 17-21,",
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