  This paper tackles the problem of constructing a non-parametric predictor
when the latent variables are given with incomplete information. The convenient
predictor for this task is the random forest algorithm in conjunction to the
so-called CART criterion. The proposed technique enables a partial imputation
of the missing values in the data set in a way that suits both a consistent
estimator of the regression function as well as a partial recovery of the
missing values. A proof of the consistency of the random forest estimator is
given in the case where each latent variable is missing completely at random
(MCAR).
