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October 2004 Wavelet-based estimation with multiple sampling rates
Peter Hall, Spiridon Penev
Ann. Statist. 32(5): 1933-1956 (October 2004). DOI: 10.1214/009053604000000751

Abstract

We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator, and decreasing it when, again using thresholded terms as an empirical guide, signal complexity is judged to have decreased. Through sampling in this way the algorithm is able to accurately recover relatively complex signals without increasing the long-run average expense of sampling. It achieves this level of performance by exploiting the opportunities for near-real time sampling that are available if one uses a relatively high primary resolution level when constructing the basic wavelet estimator. In the practical problems that motivate the work, where signal to noise ratio is particularly high and the long-run average sampling rate may be several hundred thousand operations per second, high primary resolution levels are quite feasible.

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Peter Hall. Spiridon Penev. "Wavelet-based estimation with multiple sampling rates." Ann. Statist. 32 (5) 1933 - 1956, October 2004. https://doi.org/10.1214/009053604000000751

Information

Published: October 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1056.62043
MathSciNet: MR2102498
Digital Object Identifier: 10.1214/009053604000000751

Subjects:
Primary: 62G08
Secondary: 62P30

Keywords: adaptive estimation , bandwidth , digital recording , high frequency , Nonparametric regression , online analysis , primary resolution level , sampling rule , sequential analysis , signal analysis , threshold

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 5 • October 2004
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