Bias & Variance of LOO and 3-Way: Let L be the squared loss function, f be a predictor and y be the predicted value for a particular x. Also let y* be the optimal prediction (actual response for x), and ym be the main prediction. Under squared loss function, main function becomes mean of all predictions: ym=mean(all y's). Then the following definitions follow:
- Bias(x) = L(y*, ym)
- Var(x) = ED(L(ym, y)) where D is the occurrence of x in all training sets.
- Biasavg = Ex(B(x))
- Varavg = Ex(Var(x))