Choice of the Threshold Parameter in Wavelet Function Estimation

The procedures of Donoho, Johnstone, Kerkyacharian and Picard [DJKP] estimate functions by inverting thresholded wavelet transform coefficients of the data. The choice of threshold is crucial to the success of the method and is currently subject to an intense research effort. We describe how we have applied the statistical technique of cross-validation to choose a threshold and we present results that indicate that its performance for correlated data. Finally, to illustrate the techniques, we apply various wavelet-based estimation methods to some noisy one- and two-dimensional signals and display the results.