**统计学系系列讲座之****306****期**

**时间：**2018年6月12日（周二）16:00-17:00

**地点：**史带楼303室

**主持人：**夏寅 青年研究员 复旦大学管理学院统计学系

**主题：**Determinants of Correlation Matrices with Applications

**主讲人：**Professor Tiefeng Jiang School of Statistics, University of Minnesota

**简介：**姜铁峰，美国明尼苏达大学统计学院教授，天津市千人计划入选者，主要从事概率统计理论及其相关领域的研究，特别是在概率论、高维统计学以及纯数学等交叉学科取得了突破性的进展。在国际顶尖的概率统计与机器学习杂志上发表论文40余篇，包括Ann. Probab.，Probab. Theory Rel.，Ann. Stat.，Ann. Appl. Probab.，J. Mach. Learn. Res.等。

**摘要：**Let M_n be the sample correlation matrix associated with a random sample from a p-dimensional normal distribution with correlation matrix R_n. Assume the sample size is n. The sample correlation matrix is a popular object in statistics and has many connections with mathematical and physical problems. We show that the logarithm of M_n satisfies the central limit theorem if the smallest eigenvalue of R_n is larger than 1/2 and that n and p are comparable. The result is applied to a problem in high-dimensional statistics. In addition, some new tools will be introduced.

**统计学系系列讲座之****307****期**

**时间：**2018年6月22日（周五）16:00-17:00

**地点：**史带楼503室

**主持人：**张新生 教授 复旦大学管理学院统计学系

**主题：**High-dimensional Gaussian graphical model for network-linked data

**主讲人：**Professor Ji Zhu（朱冀） Department of Statistics, University of Michigan，复旦大学管理学院“上海千人“讲座讲授。

**简介：**He received his Ph.D. in Statistics from Stanford University in 2003. He was elected a Fellow of the American Statistical Association in 2013, of the Institute of Mathematical Statistics in 2015. He has served as Associate Editor of the Journal of the American Statistical Association (2011–Now), Biometrika (2011–2015), Journal of Multivariate Analysis (2010-2011). Ji Zhu’s research has concentrated on Statistical learning and data mining High-dimensional data, Statistical network analysis, Statistics in finance and marketing, Statistical modeling in computational biology and health sciences.

**摘要：**Graphical models are commonly used in representing conditional independence between random variables, and learning the conditional independence structure from data has attracted much attention in recent years. However, almost all commonly used graph learning methods rely on the assumption that the observations share the same mean vector. In this paper, we extend the Gaussian graphical model to the setting where the observations are connected by a network and propose a model that allows the mean vectors for different observations to be different. We have developed an efficient estimation method for the model and demonstrated the effectiveness of the proposed method using simulation studies. Further, we prove that under the assumption of "network cohesion", the proposed method can estimate both the inverse covariance matrix and the corresponding graph structure accurately. We have also applied the proposed method to a dataset consisting of statisticians' coauthor ship network to learn the statistical term dependency based on the authors' publications and obtained meaningful results. This is joint work with Tianxi Li, Cheng Qian and Elizaveta Levina.

**统计学系系列讲座之****308****期**

**时间：**2018年6月27日（周三）15:30-16:30

**地点：**史带楼205室

**主持人：**黎德元 教授 复旦大学管理学院统计学系

**主题：**Automatic Shape-constrained Nonparametric Regression

**主讲人：**Prof. Huixia Judy Wang George Washington University, USA

**摘要：**Shape information such as monotonicity and convexity of regression functions, if available, can be incorporated in nonparametric regression to improve estimation accuracy. However, in practice, the functional shapes are not always known in advance. On the other hand, using hypothesis testing to determine shapes would require testing various null and alternative hypotheses, and thus is not practical when interests are on many functional curves. To overcome this challenge, we propose a new penalization-based method, which provides function estimation and automatic shape identification simultaneously. The method estimates the functional curve through quadratic B-spline approximation, and captures the shape feature by penalizing the positive and negative parts of the first two derivatives of the spline function in a group manner. Under some regularity conditions, we show that the proposed method can identify the correct shape with probability approaching one, and the resulting nonparametric estimator can achieve the optimal convergence rate. Simulation shows that the proposed method gives more stable curve estimation and more accurate shape identification than the unconstrained B-spline estimator, and it is competitive to the shape-constrained estimator assuming prior knowledge of the functional shape. The proposed method is applied to a motivating vocalization study to examine the effect of Mecp2 gene on the vocalizations of mice during courtship.

**统计学系系列讲座之****309****期**

**时间：**2018年7月4日（周三）16:00-17:00

**地点：**史带楼801室

**主持人：**张新生 教授复旦大学管理学院统计学系

**主题：**Local False Discovery Rate Based Methods for Multiple Testing of One-Way Classiﬁed Hypotheses

**主讲人：**Professor Sanat K. Sarkar Department of Statistical Science, Temple University

**简介：** Dr. Sanat K. Sarkar is an internationally recognized researcher who has made fundamental contributions to the development of the field of multiple testing toward its applications in modern scientific investigations, such as in genomics and brain imaging. His research has been funded by the National Science Foundation and the National Security Agency, and often been cited in peer-reviewed journals. He has delivered invited talks at numerous national and international conferences. He co-organized a major conference on Multiple Comparisons funded by the NSF-CBMS and served on the organizing committees of several international conferences on the same topic. He has served on the editorial boards of several respectable journals, like the Annals of Statistics, the American Statistician, and Sankhya. Dr. Sarkar has been recognized as a fellow by both the Institute of Mathematical Statistics and the American Statistical Association, and as an elected member of the International Statistical Institute. He was awarded the Musser Award for excellence in research by the Fox School and inducted several times to the Dean’s Research Honor Roll.

**摘要：**In this talk, a novel framework for multiple testing of hypotheses grouped in a one-way classiﬁed form using hypothesis-speciﬁc local false discovery rates (Lfdr’s) is given. It is built on an extension of the standard two-class mixture model from single to multiple groups, deﬁning hypothesis-speciﬁc Lfdr as a function of the conditional Lfdr for the hypothesis given that it is within a signiﬁcant group and the Lfdr for the group itself and involving a new parameter that measures grouping eﬀect. This deﬁnition captures the underlying group structure for the hypotheses belonging to a group more eﬀectively than the standard two-class mixture model. Two new Lfdr based methods, possessing meaningful optimalities, are produced in their oracle forms. One, designed to control false discoveries across the entire collection of hypotheses, is proposed as a powerful alternative to simply pooling all the hypotheses into a single group and using commonly used Lfdr based method under the standard single-group two-class mixture model. The other is proposed as an Lfdr analog of the method of Benjamini & Bogomolov (2014) for selective inference. It controls Lfdr based measure of false discoveries associated with selecting groups concurrently with controlling the average of within-group false discovery proportions across the selected groups. Numerical studies show that our proposed methods are indeed more powerful than their relevant competitors, at least in their oracle forms, in commonly occurring practical scenarios.

**统计学系系列讲座之****310****期**

**时间：**2018年6月25日（周一）16:00-17:00

**地点：**史带楼205室

**主持人：**朱仲义 教授复旦大学管理学院统计学系

**主题：**Model-Free Causal Inference in Observational Studies

**主讲人：**Professor Ying Zhang Department of Biostatistics, Indiana University

**简介：**Dr. Ying Zhang is Professor and Director of Biostatistics Education in Department of Biostatistics at Indiana University. He received his Ph.D in Statistics from University of Washington in 1998 and is an elected Fellow of American Statistical Association (ASA). He has a broad research interest in statistical methodologies including non-/semi-parametric inference, panel count and interval-censored data analysis, statistical computing and data mining, design of clinical trial and casual inference. He is a well-funded statistician for Huntington Disease Research. He has a strong publication record in top-tier statistical journals such as Annals of Statistics, Journal of American Statistical Association, Biometrika, Biometrics and Statistica Sinica.

**摘要：**Causal inference is a key component for comparative effectiveness research in observational studies. The inverse-propensity weighting (IPW) technique and augmented inverse-propensity weighting (AIPW) technique, which is known as a double-robust method, are the common methods for making causal inference in observational studies. However, these methods are known not stable, particularly when the models for propensity score and the study outcome are wrongly specified. In this work, we propose a model-free approach for causal inference. While possessing standard asymptotic properties, this method also enjoys excellent finite sample performance and robustness. Simulation studies were conducted to compare with the well-known IPW and AIPW methods for causal inference. A real-life example from an ongoing Juvenile Idiopathic Arthritis Study was applied for the illustration of the proposed method.

统计学系

2018-6-11