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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
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