The Annals of Statistics

Wavelet-based estimation with multiple sampling rates

Peter Hall and Spiridon Penev

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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.

Article information

Ann. Statist., Volume 32, Number 5 (2004), 1933-1956.

First available in Project Euclid: 27 October 2004

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Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression
Secondary: 62P30: Applications in engineering and industry

Adaptive estimation bandwidth digital recording high frequency nonparametric regression online analysis primary resolution level sampling rule signal analysis threshold sequential analysis


Hall, Peter; Penev, Spiridon. Wavelet-based estimation with multiple sampling rates. Ann. Statist. 32 (2004), no. 5, 1933--1956. doi:10.1214/009053604000000751.

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