Adaptive estimation of multivariate piecewise polynomials and bounded variation functions by optimal decision trees
用最优决策树自适应估计多元分段多项式与有界变差函数
Proposed by Donoho (Ann. Statist. 25 (1997) 1870–1911), Dyadic CART is a nonparametric regression method which computes a globally optimal dyadic decision tree and fits piecewise constant functions in two dimensions. In this article, we define and study Dyadic CART and a closely related estimator, namely Optimal Regression Tree (ORT), in the context of estimating piecewise smooth functions in general dimensions in the fixed design setup. More precisely, these optimal…