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

On the Consistency of a Random Forest Algorithm in the Presence of Missing Entries