Analysis of statistical properties of the hybrid thresholding technique

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.