摘要：This paper introduces a novel nonparametric method for estimating high-dimensional dynamic covariance matrices with multiple conditioning covariates, leveraging random forests and supported by robust theoretical guarantees. Unlike traditional static methods, our dynamic nonparametric covariance models effectively capture distributional heterogeneity. Furthermore, unlike kernel-smoothing methods, which are restricted to a single conditioning covariate, our approach accommodates multiple covariates in a fully nonparametric framework. To the best of our knowledge, this is the first method to use random forests for estimating high-dimensional dynamic covariance matrices. In high-dimensional settings, we establish uniform consistency theory, providing nonasymptotic error rates and model selection properties, even when the response dimension grows sub-exponentially with the sample size. These results hold uniformly across a range of conditioning variables. The method’s effectiveness is demonstrated through simulations and a stock dataset analysis, highlighting its ability to model complex dynamics in high-dimensional scenarios. This is a joint work with Shuguang Yu, Fan Zhou, Yingjie Zhang and Hongtu Zhu.

个人简介：谌自奇，华东师范大学统计学院研究员，紫江青年学者，博士生导师。博士毕业于东北师范大学，曾在美国安德森癌症研究中心生物统计系从事博士后研究工作。研究兴趣包含高维统计、因果结果学习、机器学习、生物医学统计等。以第一或通讯作者在JASA、Biometrics、NeurIPS、AAAI等国际权威统计或者计算机期刊（会议）上发表论文20多篇。主持国家自然科学基金面上项目2项、国家自然科学基金重点项目（子课题）1项，国家自然科学基金青年项目1项等，作为骨干力量参与国家重点研发计划和上海市“科技创新行动计划”基础研究领域应用数学重点项目。