统计学系系列讲座之360期

统计学系系列讲座之360期

时　间：2019年12月6日（星期五）9:30-10:30

地　点：思源教授楼726室

主持人：朱仲义  教授 复旦大学管理学院统计学系

主　题：Modelling function-valued processes with non-separable and/or non-stationary covariance structure

主讲人：Dr Jian Qing Shi

              School of Mathematics, Statistics and Physics, Newcastle University, UK and Alan Turing Institute, UK

摘　要：

Separability of the covariance structure is a common assumption for function-valued processes defined on two- or higher-dimensional domains. This assumption is often made to obtain an interpretable model or due to difficulties in modelling a potentially complex covariance structure, especially in the case of sparse designs. We proposed to use Gaussian processes with flexible parametric covariance kernels which allow interactions between the inputs in the covariance structure. When we use suitable covariance kernels, the leading eigen-surfaces of the covariance operator can explain well the main modes of variation in the functional data, including the interactions between the inputs. The results are demonstrated by simulation studies and by applications to real world data.

统计学系系列讲座之361期

时　间：2019年12月6日（星期五）10:30-11:30

地　点：思源教授楼726室

主持人：朱仲义  教授 复旦大学管理学院统计学系

主　题：Category-Adaptive Variable Screening for Ultra-high Dimensional Heterogeneous Categorical Data

主讲人：唐年胜 教授 云南大学数学与统计学院

简　介：唐年胜，博士，国家杰出青年科学基金获得者，教育部“**学者”特聘教授，教育部“新世纪优秀人才”，云南省科技领军人才，云南省首批云岭学者，云南省中青年学术和技术带头人，云南省教学名师，云南省学位委员会经济与管理学科评议组成员，博士生导师。 云南省高校“统计与信息技术重点实验室 ” 负责人，“云南大学复杂数据统计推断方法研究 ” 省创新团队带头人。

摘　要：

The populations of interest in modern studies are very often heterogeneous. The population heterogeneity, the qualitative nature of the outcome variable and the high dimensionality of the predictors pose significant challenge in statistical analysis. In this article, we introduce a category-adaptive screening procedure with high-dimensional heterogeneous data, which is to detect category-specific important covariates. The proposal is a model-free approach without any specification of a regression model and an adaptive procedure in the sense that the set of active variables is allowed to vary across different categories, thus making it more flexible to accommodate heterogeneity.

For response-selective sampling data, another main discovery of this paper is that  the proposed method works directly without any modification. Under mild regularity conditions, the newly procedure is shown to possess the sure screening and ranking consistency properties. Simulation studies contain supportive evidence  that the proposed method performs well under various settings and it is effective to extract category-specific information. Applications are illustrated with two real data sets.

 统计学系 

2019-12-4