PRESS statistic for ridge regression

In ordinary least squares, regressing a target vector $y$ against a set of predictors $X$, the hat matrix is computed as

$$H = X (X^tX)^{-1} X^t$$

and the PRESS (predicted residual sum of squares) is calculated by

$$SS_P = \sum_i \left( \frac{e_i}{1-h_{ii}}\right)^2$$

where $e_i$ is the $i$th residual and the $h_{ii}$ are the diagonal elements of the hat matrix.

In ridge regression with penalty coefficient $\lambda$, the hat matrix is modified to be

$$H = X (X^t X + \lambda I)^{-1} X^t$$

Can the PRESS statistic be calculated in the same way, using the modified hat matrix?