Limit distribution of a risk estimate using the vaguelette-wavelet decomposition of signals in a model with correlated noise

A signal function after the application of a linear homogenous operator in a model with correlated noise is estimated. The asymptotic properties of a risk estimate with thresholding of the coefficients of the vaguelette-wavelet decomposition of a signal are considered. Conditions for the asymptotic normality of the risk estimate are proposed.