THE COMPARISON OF DIFFERENT THRESHOLD RULES IN ESTIMATING THE WAVELET REGRESSION FUNCTION

Abstract

The applications of wavelet regression began to enter the field of statistics as a powerful tool in the field of data smoothing. Considering the wavelet method in statistical estimates is one of the very powerful methods that have been spread by means of wavelet shrinkage estimators (Estimators (Wavelet Shrinkage Donoho and Johnstone (1994) and Donoho et al. (1995) estimators have been introduced. Non-linear wavelet in non-parametric regression The wavelet reduction technique is one of the best techniques used in estimating the non-parametric regression function, but it is affected in the method of selecting the appropriate rules and threshold values. Semi-smooth and the second improved threshold In addition to taking the values of Visus hrink and sure shrink threshold values, using three test functions and sample sizes (64, 128, 256, 512) and different noise ratios. The soft thresholds smi rule is followed by the improved method M2 using the visu threshold value. It usually breaks down with the extreme difficulty of providing a suitable threshold value for the wavelet threshold coefficients at all desired levels. This prompted the researchers to find functions and threshold values that suit that problem to obtain efficient wavelet estimations using deflated wavelet regression and different threshold rules