  The issue of estimating residual variance in regression models has
experienced relatively little attention in the machine learning community.
However, the estimate is of primary interest in many practical applications,
e.g. as a primary step towards the construction of prediction intervals. Here,
we consider this issue for the random forest. Therein, the functional
relationship between covariates and response variable is modeled by a weighted
sum of the latter. The dependence structure is, however, involved in the
weights that are constructed during the tree construction process making the
model complex in mathematical analysis. Restricting to L2-consistent random
forest models, we provide random forest based residual variance estimators and
prove their consistency.
