主讲人

朱仲义

讲座时间

2021.3.29  10：30-11：30

地点

综合楼650

摘要

Quantile regression is an indispensable tool for statistical learning. Traditional  quantile regression methods consider vector-valued covariates and estimate the corresponding coefficient vector. Many modern applications involve data with a tensor structure. In this paper, we propose a quantile regression model which takes tensors as covariates, and present an estimation approach based on Tucker decomposition. It effectively reduces the number of parameters, leading to efficient estimation and feasible computation. We also use a sparse Tucker decomposition, which is a popular approach in the literature, to further reduce the number of parameters when the dimension of the tensor is large. We propose an alternating update algorithm combined with alternating direction method of multipliers (ADMM). The asymptotic properties of the estimators are established under suitable conditions. The numerical performances are demonstrated via simulations and an application to a crowd density estimation problem.

主讲人简介

复旦大学统计系教授，博士研究生导师；曾任中国概率统计学会第八、九届副理事长,国际著名杂志“Statistica Sinica”副主编; “应用概率统计”, ”数理统计与管理”杂志编委，中国统计教材编审委员会委员；现为国际数理统计学会当选会员，”中国科学：数学”杂志编委。专业研究方向为：保险精算；纵向数据(面板数据)模型；分位数回归模型等。主持完成国家自然科学基金五项、国家社会科学基金一项，作为子项目负责人完成国家自然科学基金重点项目一项。目前主持国家自然科学基金重大项目子项目一项，重点项目子项目一项，面上项目一项。近几年发表论文100多篇(其中包括在国际四大统计顶级刊物等SCI论文六十多篇)。获得教育部自然科学二等奖一次。