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

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  • Ramosaj, Burim
  • Pauly, Markus

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.

Suggested Citation

  • Ramosaj, Burim & Pauly, Markus, 2019. "Consistent estimation of residual variance with random forest Out-Of-Bag errors," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 49-57.
    • Handle: RePEc:eee:stapro:v:151:y:2019:i:c:p:49-57
    DOI: 10.1016/j.spl.2019.03.017
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    References listed on IDEAS

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    1. Stefan Wager & Susan Athey, 2018. "Estimation and Inference of Heterogeneous Treatment Effects using Random Forests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1228-1242, July.
    2. Scornet, Erwan, 2016. "On the asymptotics of random forests," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 72-83.
    3. Biau, Gérard & Devroye, Luc, 2010. "On the layered nearest neighbour estimate, the bagged nearest neighbour estimate and the random forest method in regression and classification," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2499-2518, November.
    4. Lin, Yi & Jeon, Yongho, 2006. "Random Forests and Adaptive Nearest Neighbors," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 578-590, June.
    5. Mendez, Guillermo & Lohr, Sharon, 2011. "Estimating residual variance in random forest regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2937-2950, November.
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