Wavelet-based estimation with multiple sampling rates

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dc.creatorHall, Peter
dc.creatorPenev, Spiridon
dc.date2005-03-29
dc.date.accessioned2026-07-07T08:06:45Z
dc.date.available2026-07-07T08:06:45Z
dc.descriptionWe 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.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053604000000751 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0503669
dc.identifierhttp://arxiv.org/abs/math/0503669
dc.identifierAnnals of Statistics 2004, Vol. 32, No. 5, 1933-1956
dc.identifierdoi:10.1214/009053604000000751
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130718
dc.subjectStatistics Theory
dc.subject62G08 (Primary) 62P30 (Secondary)
dc.titleWavelet-based estimation with multiple sampling rates
dc.typetext

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