Wavelet Toolbox

One-Dimensional Estimation Using the GUI for Randomly Spaced Observations (Stochastic Design)

1. From the File menu, choose the Load Data for Stochastic Design Regression option. When the Load data for Stochastic Design Regression dialog box appears, select the demo MAT-file ex1nsto.mat, which should reside in the MATLAB directory toolbox/wavelet/wavedemo. Click the OK button. This short set of data (of size 500) is loaded into the Regression Estimation 1-D -- Stochastic Design tool.

   

The loaded data denoted (X,Y), the histogram of X, and the processed data obtained after a binning are displayed. The histogram is interesting, because the values of X are randomly distributed. The binning step is essential since it transforms a problem of regression estimation for irregularly spaced X data into a classical fixed design scheme for which fast wavelet transform can be used.

2. Select the sym4 wavelet from the Wavelet menu, select 5 from the Level menu, and enter 125 in the Nb bins edit box. Click the Decompose button. The tool displays the detail coefficients of the decomposition.
3. From the Select thresholding method menu, select the item Penalize low and click the Estimate button.

   

4. Check Show Estimated Function to validate the fit of the original data.

   

One-Dimensional Estimation Using the GUI for Equally Spaced Observations (Fixed Design)

Importing and Exporting Information from the Graphical Interface