High-dimensional data pose many challenges to traditional statistical and computational methods. Specifically, due to the small sample size, there are more uncertainties associated with standard estimations of parameters such as the mean and variance estimations. As a consequence, statistical analyses based on such parameter estimation are usually unreliable. To obtain more accurate parameter estimation some statistical methods, such as regularization through shrinkage, may yield better results. In this talk, I will first review some new developments in shrinkage estimation on variances, under the framework of microarray data analysis. I will then introduce a recent work of mine that develops the shrinkage estimation of the population mean under the quadratic loss function for high-dimensional data. For illustration, a shrinkage-based diagonal discriminant rule will be proposed and it will be demonstrated to outperform the existing competitor in a wide range of settings.

题目：Estimation of Partially Linear Regression Model under Partial Consistency Property报告人：Professor Heng PENG(香港浸会大学教授)AbstractClassic linear regression models are often criticized for requiring a response surface to be linear and additive in predictors. To ameliorate this problem, partially linear model of the form Y=Xβ+g(Z) was proposed to reduced bias. The nonparametric es...

报 告 人：沈 纯 理 教授（华东师范大学数学系）报告题目：图像处理中与微分几何相关的一些问题报告时间：2013年3月15日（周五）下午4:00-5:00报告地点：致远楼107

一方面由于存在各种不确定因素使得已有的数学模型很难应用到实际工业过程中;另一方面，传感器的飞速发展使得人们可以获得大量数据，所以基于数据的建模是当前研究的热点问题。本报告简要介绍数据驱动的工过程业的建模和监测

复杂多个体系统由大量个体通过局部相互作用而形成一个整体并在系统层次上涌现出各种各样的群体行为，如同步、群体智能等。复杂多个体系统在飞行器编队控制、多机器人协调等上有广阔的应用前景。本报告简要介绍复杂多个体系统的建模、分析与应用。

In this talk, we will discuss the recursive filtering problem for nonlinear stochastic systems with randomly occurring incomplete information. We will address the quantized filtering problem, the extended Kalman filtering problem, the recursive filtering problem with random parameter matrices, the gain-constrained recursive filtering problem and the probability-guaranteed filtering problems. The incomplete information includes multiple missing measurements, fading measurements, quantization effects, probabilistic sensor delays, sensor saturations, etc. Both the theoretical research and engineering applications will be discussed, and a series of recently published results will be reported.

Starting with the toy example of a star-shaped frame for the plane (e.g. sea star), we explain the powerful role operator-valued measure, and particularly coherent states (CS) can play in quantizing any set equipped with a measure. These integral quantizations are illustrated with the standard case involving the Weyl-Heisenberg group (yielding the canonical quantization), and with the case involving for affine group of the real line.

报 告 人：纪春岗 教授（南京师范大学williamhill体育在线登录）报告题目：Sums of Squares of Cyclotomic Fields时间：2013年1月17日（周四）上午10:00-11:00报告地点：致远楼105