I'm using ridge regression for estimating the fair value of variable $Y$ against a vector of correlated predictor variables $X_i$, based on past observations of both $Y$ and $X_i$. Let's assume that both Y and Xi are standardized (mean $= 0$, std $= 1$).
Problem is that ridge regression introduces bias into the estimate of $Y$, and the further the predictor vector is from zero, the greater the bias. In order to correct for the bias, I perform another regression of $Y$ onto one variable, which is the linear sum of predictors with coefficients calculated from the ridge regression.
It seems that this procedure both benefits from the stable coefficients calculated using ridge and from the subsequent bias-correction, which looks like a double win.
Is this procedure "valid"? Does anybody do the same? Is there any literature on such kind of bias correction?