Mean-square thresholding risk with a random sample size

Nonlinear methods of signal de-noising based on the threshold processing of wavelet coefficients are widely used in various application areas. These methods have gained their popularity due to the speed of the algorithms for constructing estimates and the possibility of adapting to functions belonging to different classes of regularity better than linear methods. When applying thresholding techniques, it is usually assumed that the number of wavelet coefficients is fixed and the noise distribution is Gaussian. This model has been well studied in the literature, and optimal threshold values have been calculated for different classes of signals. However, in some situations, the sample size is not known in advance and is modeled by a random variable. The present author considers a model with a random number of observations containing Gaussian noise and estimates the order of the mean-square risk with increasing sample size.