Asymptotic Normality for Multivariate Random Forest Estimators
Regression trees and random forests are popular and effective non-parametric estimators in practical applications. A recent paper by Athey and Wager shows that the random forest estimate at any point is asymptotically Gaussian; in this paper, we extend this result to the multivariate case and show that the vector of estimates at multiple points is jointly normal. Specifically, the covariance matrix of the limiting normal distribution is diagonal, so that the estimates at any two points are independent in sufficiently deep trees. Moreover, the off-diagonal term is bounded by quantities capturing how likely two points belong to the same partition of the resulting tree. Our results relies on certain a certain stability property when constructing splits, and we give examples of splitting rules for which this assumption is and is not satisfied. We test our proposed covariance bound and the associated coverage rates of confidence intervals in numerical simulations.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Asymptotic normality of robust $M$-estimators with convex penalty
This paper develops asymptotic normality results for individual coordinates of robust M-estimators with convex penalty in high-dimensions, where the dimension $p$ is at most of the same order as the sample size $n$, i.e,…
Debiased Nonparametric Regression for Statistical Inference and Distributionally Robustness
This study proposes a debiasing method for smooth nonparametric estimators. While machine learning techniques such as random forests and neural networks have demonstrated strong predictive performance, their theoretical …
regressionA classification point-of-view about conditional Kendall's tau
We show how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. Conditional Kendall's tau is a conditional dependence parameter that is a characteristic of a given pair of rando…
ClassificationGeneral ClassificationAsymptotic Distributions and Rates of Convergence for Random Forests via Generalized U-statistics
Random forests remain among the most popular off-the-shelf supervised learning algorithms. Despite their well-documented empirical success, however, until recently, few theoretical results were available to describe thei…
Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs
We introduce a multivariate local-linear estimator for multivariate regression discontinuity designs in which treatment is assigned by crossing a boundary in the space of running variables. The dominant approach uses the…
regressionvalid