时 间：2023年12月14日 13:00-14:00
地 点: 腾讯会议ID：910-209-408
报告人：赵俊龙北京师范大学教授
主持人：项冬冬 华东师范大学教授
摘 要：
High dimensional linear models are commonly used in practice. In many applications, one is interested in linear transformations $\bbeta^\top x$ of regression coefficients $\bbeta\in \mR^p$, where $x$ is a specific point and is not required to be identically distributed as the training data. One common approach is the plug-in technique which first estimates $\bbeta$, then plugs the estimator in the linear transformation for prediction. Despite its popularity, estimation of $\bbeta$ can be difficult for high dimensional problems. Commonly used assumptions in the literature include that the signal of coefficients $\bbeta$ is sparse and predictors are weakly correlated. These assumptions, however, may not be easily verified, and can be violated in practice. When $\bbeta$ is non-sparse or predictors are strongly correlated, estimation of $\bbeta$ can be very difficult. In this paper, we propose a novel pointwise estimator for linear transformations of $\bbeta$. This new estimator greatly relaxes the common assumptions for high dimensional problems, and is adaptive to the degree of sparsity of $\bbeta$ and strength of correlations among the predictors. In particular, $\bbeta$ can be sparse or non-sparse and predictors can be strongly or weakly correlated. The proposed method is simple for implementation. Numerical and theoretical results demonstrate the competitive advantages of the proposed method for a wide range of problems.
报告人简介：
赵俊龙北京师范大学统计学院教授。研究方向主要为高维数据分析、统计机器学习、稳健统计等。发表相关论文SCI论文近五十篇，部分结果发表在统计学顶级期刊Journal of the Royal Statistical Society: Series B（JRSSB）、 The Annals of Statistics（AOS）、Journal of American Statistical Association(JASA)，Biometrika上。主持多项国家自然科学基金项目。