B0835
Title: Random forest weighted local Frechet regression with random objects
Authors: Rui Qiu - East China Normal University (China) [presenting]
Zhou Yu - East China Normal University (China)
Ruoqing Zhu - University of Illinois at Urbana-Champaign (United States)
Abstract: Statistical analysis is increasingly confronted with complex data from metric spaces. The seminal work of Frechet regression has provided a general paradigm for modelling complex metric space-valued random objects given Euclidean predictors. However, the local approach therein involves nonparametric kernel smoothing and suffers from the curse of dimensionality. A novel random forest-weighted local Frechet regression paradigm is proposed to address this issue. The main mechanism of the approach relies on a locally adaptive kernel generated by random forests. The first method utilizes these weights as the local average to solve the conditional Frechet mean. In contrast, the second method performs local linear Frechet regression, significantly improving existing Frechet regression methods. Based on the theory of infinite order U-processes and infinite order $M_{m_n}$-estimator, the consistency, rate of convergence, and asymptotic normality for the local constant estimator is established, which covers the current large sample theory of random forests with Euclidean responses as a special case. Numerical studies show the superiority of the methods with several commonly encountered types of responses, such as distribution functions, symmetric positive-definite matrices, and sphere data. The practical merits of the proposals are also demonstrated through the application of human mortality distribution data and New York taxi data.
