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A Tuning-free Robust and Efficient Approach to High-dimensional Regression

主讲人: 李润泽
主讲人简介:

李润泽是宾州州立大学统计系讲席教授。他的研究方向包括高维数据变量选择及统计推断,非参数和半参数建模和统计推断,统计在社会及行为科学研究的应用。他曾担任Annals of Statistics的主编。现在是Journal of American Statistical Association和其他刊物的副主编。他是IMS, ASA和 AAAS的fellow。他的其他荣誉,发表的文章等信息见在他的个人网页:http://www.personal.psu.edu/ril4/

主持人: 钟威
简介:

We introduce a novel approach for high-dimensional regression with theoretical guarantees. The new procedure overcomes the challenge of tuning parameter selection of Lasso and possesses several appealing properties. It uses an easily simulated tuning parameter that automatically adapts to both the unknown random error distribution and the correlation structure of the design matrix. It is robust with substantial efficiency gain for heavy-tailed random errors while maintaining high efficiency for normal random errors. Comparing with other alternative robust regression procedures, it also enjoys the property of being equivariant when the response variable undergoes a scale transformation. Computationally, it can be efficiently solved via linear programming. Theoretically, under weak conditions on the random error distribution, we establish a finite-sample error bound with a near-oracle rate for the new estimator with the simulated tuning parameter. Our results make useful contributions to mending the gap between the practice and theory of Lasso and its variants. We also prove that further improvement in efficiency can be achieved by a second-stage enhancement with some light tuning. Our simulation results demonstrate that the proposed methods often outperform cross-validated Lasso in various settings.

时间: 2020-07-03(Friday)09:30-11:00
地点: 线上腾讯会议(会议号邮件另行通知)
期数: 统计与数据科学前沿系列讲座第三讲
主办单位: 厦门大学经济学院、王亚南经济研究院
类型: 系列讲座
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