Geodesic
Analysis of statistical properties of the hybrid thresholding technique
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2019), pp. 15-22

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We consider the problem of constructing an estimate of the signal function using the method of hybrid threshold processing of wavelet expansion coefficients. Hybrid threshold processing is a compromise between soft and hard threshold processing, which combines the main advantages of these two methods. In the data model with an additive noise, an unbiased estimate of the mean-square risk is analyzed and it is shown that under certain conditions this estimate is strongly consistent and asymptotically normal. These properties allow to use the risk estimate as a criterion for the quality of a method and to construct asymptotic confidence intervals for the theoretical mean-square risk.
Keywords: wavelets, hybrid thresholding, risk estimate, limit theorems. 
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     author = {P. S. Popenova and O. V. Shestakov},
     title = {Analysis of statistical properties of the hybrid thresholding technique},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {15--22},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2019_1_a1/}
}
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P. S. Popenova; O. V. Shestakov. Analysis of statistical properties of the hybrid thresholding technique. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2019), pp. 15-22. http://geodesic.mathdoc.fr/item/VTPMK_2019_1_a1/