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20151224第四场统计与大数所学术讲座会（统计与大数据理论与方法小型研讨会）

时间：2015-12-23

**演讲人: Oliver Linton**

剑桥大学三一学院Fellow，政治经济学教授

Co-Editor, Journal of Econometrics, 2014-

Co-Editor, Econometric Theory, 2000-

Co-Editor, Econometrics Journal, 2007-2014

Associate Editor, Econometrica , 2003-2006, 2006-2009, 2009-2012, 2012-2015

Associate Editor, Journal of the American Statistical Association

Case Studies and Applications, 2004-2007

Associate Editor, Journal of Econometrics, 1998-2007, 2012-

Guest Co-Editor (with J.P. Florens), Special Issue of Econometric Theory on Inverse Problems,

2008

Guest Co-Editor, Special Issues of Journal of Econometrics, 2004, 2006, 2010

Editorial Board, Review of Economic Studies, 1999-2006

Associate Editor, Journal of Statistical Planning and Inference, 2001

Associate Editor, Econometric Theory, 1996-1999

**演讲题目: **Multivariate Variance Ratio Statistics

**摘要:** TBA

**时间: 2015年12月24日 14:00-14:50**

**地点: 明德主楼1030会议室**

**演讲人:薛凌洲**

宾夕法尼亚州立大学统计系助理教授

2015-2018, National Science Foundation (NSF) Division Of Mathematical Sciences (DMS) Award

2014-2016, American Mathematical Society (AMS) Simons Travel Grant

2014, Institute of Mathematical Statistics (IMS) Travel Award

2011, International Biometric Society ENAR Distinguished Student Paper Award

2010, American Statistical Association Student Paper Competition Winner

2010, Best Poster Award, "Borrowing Strength: Theory Powering Applications" Conference

**演讲题目:** Sufficient Forecasting Using Factor Models

**摘要:** We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting method called the sufficient forecasting, which provides a set of sufficient predictive indices, inferred from high-dimensional predictors, to deliver additional predictive power. The projected principal component analysis will be employed to enhance the accuracy of inferred factors when a semi-parametric (approximate) factor model is assumed. Our method is also applicable to cross-sectional sufficient regression using extracted factors. {The connection between the sufficient forecasting and the deep learning architecture is explicitly stated.} The sufficient forecasting correctly estimates projection indices of the underlying factors even in the presence of a nonparametric forecasting function. The proposed method extends the sufficient dimension reduction to high-dimensional regimes by condensing the cross-sectional information through factor models. We derive asymptotic properties for the estimate of the central subspace spanned by these projection directions as well as the estimates of the sufficient predictive indices. We further show that the natural method of running multiple regression of target on estimated factors yields a linear estimate that actually falls into this central subspace. Our method and theory allow the number of predictors to be larger than the number of observations. We finally demonstrate that the sufficient forecasting improves upon the linear forecasting in both simulation studies and an empirical study of forecasting macroeconomic variables.

This talk will be based on several joint works with Jianqing Fan, Wei Luo, and Jiawei Yao.

**时间: 2015年12月24日 15:00-15:50**

**地点: 明德主楼1030会议室**

**演讲人: 张凯**

北卡罗来纳大学教堂山分校统计与运筹系助理教授

R. J. Reynolds Industries Junior Faculty Development Award, UNC-CH, 2014.

Laha Travel Award, Institute of Mathematical Statistics, 2011.

Deming Student Scholar Award, 67th Deming Conference on Applied Statistics, 2011.

J. Parker Bursk Memorial Prize (for excellence in research), Statistics Department, The Wharton School, University of Pennsylvania, 2010.

**演讲题目:** Spherical Cap Packing Asymptotics and Rank-Extreme Detection

**摘要:** We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic universal uniform sharp bound on the maximal inner product between any set of unit vectors and a stochastically independent uniformly distributed unit vector. When the set of unit vectors are themselves independently uniformly distributed, we further develop the extreme value distribution limit of the maximal inner product, which characterizes its stochastic uncertainty around the bound.

As applications of the above asymptotic results, we derive (1) an asymptotic universal uniform sharp bound on the maximal spurious correlation, as well as its uniform convergence in distribution when the explanatory variables are independently Gaussian; and (2) a sharp universal bound on the maximum norm of a low-rank elliptically distributed vector, as well as related limiting distributions. With these results, we develop a fast detection method for a low-rank in high dimensional Gaussian data without using the spectrum information.

**时间: 2015年12月24日 16:00-16:50**

**地点: 明德主楼1030会议室**