Quantitative L2 Approximation Error of a Probability Density Estimate Given by It Samples
Thierry Blu, EPFL LIB

Test Run • 10 May 2004 • BM 4.235

Abstract
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.