Abstract:
Wavelet analysis algorithms in combination with threshold
processing procedures are widely used in nonparametric regression
problems when estimating the signal function from noisy data. The
advantages of these methods are their computational efficiency and
the ability to adapt to the local features of the function being
estimated. The error analysis of threshold processing methods is an
important practical task, since it allows assessing the quality of both
the methods themselves and the equipment used. Sometimes, the nature of
the data is such that observations are recorded at random times. If the
sampling points form a variation series constructed from a sample
of a uniform distribution over the data recording interval, then the use
of conventional threshold processing procedures is adequate. In this paper,
the author analyzes the estimate of the mean square risk of
threshold processing
and shows that under certain conditions,
this estimate is strongly consistent and asymptotically normal.
Keywords:wavelets, threshold processing, random samples, mean square risk estimate.
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