Consistent estimation of residual variance with random forest Out-Of-Bag errors

Burim Ramosaj and Markus Pauly

Statistics & Probability Letters, 2019, vol. 151, issue C, 49-57

Abstract: The issue of estimating residual variance in regression models with unknown and eventually complex link-function is still an open problem. Predictions of such outcomes are usually conducted by black-box procedures without seriously restricting the link-function class. However, quantifying uncertainty by means of residual variance estimators 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.

Keywords: Residual variance; Consistency; Out-Of-Bag samples; Random forest; Statistical learning (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.03.017

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