Regression criterion functions for the adaptive wavelet algorithm

3 Regression criterion functions for the adaptive wavelet algorithm 

A suitable criterion function for regression analysis should reflect how well the response values are predicted. In the adaptive wavelet algorithm, the criterion function considered for regression is based on the PRESS statistic and is then converted to a leave-one-out cross-validated R-squared measure as follows 

The formulation of Eq. (6) using the hat matrix makes the leave-out-one method of cross-validation quite a useful and relatively inexpensive procedure to employ. 

The cross-validated R-squared criterion function is defined as 

The actual regression model used for predicting the response is 

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