Estimating residual variance in random forest regression
Random forest, a data-mining technique which uses multiple classification or regression trees, is a popular algorithm used for prediction. Inference and goodness-of-fit assessment, however, may require an estimator of variability; in many applications the residual variance is of primary interest. This paper proposes two estimators of residual variance for random forest regression that take advantage of byproducts of the algorithm. The first estimator is based on the residual sum of squares from a random forest fit and uses a bootstrap bias correction. The second estimator is a difference-based estimator that uses proximity measures as weights. The estimators are evaluated through Monte Carlo simulations. Applications of the methods to the problem of assessing the relative variability of males and females on cognitive and achievement tests are discussed, and the methods are applied to estimate the residual variance in test scores for male and female students on the mathematics portion of the 2007 Arizona Instrument to Measure Standards.
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- Spokoiny, Vladimir, 2002. "Variance Estimation for High-Dimensional Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 111-133, July.
- Shoemaker L.H., 2003. "Fixing the F Test for Equal Variances," The American Statistician, American Statistical Association, vol. 57, pages 105-114, May.
- Cahoy, Dexter O., 2010. "A bootstrap test for equality of variances," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2306-2316, October.
- 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.
- 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.
- Tiejun Tong & Yuedong Wang, 2005. "Estimating residual variance in nonparametric regression using least squares," Biometrika, Biometrika Trust, vol. 92(4), pages 821-830, December.
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