主 题：Sublinear expectation linear regression
主讲人：林路教授
主持人：马铁丰副教授
时 间：2013年11月8日下午3:40-4:40
地 点：通博楼B座212学术会议室
主办单位：统计学院统计研究中心 科研处
主讲人简介：
林 路，教授，博士生导师，山东大学金融研究院副院长。2001年毕业于南开大学概率与统计科学博士。研究兴趣：非参数统计，稳健统计，金融统计，高维模型。现已在Annals of Statistics及Computational Statistics & Data Analysis等国际杂志发表论文60余篇。
内容提要：
Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and econometrics. Under the nonlinear expectation framework, however, the related statistical models and statistical inferences have not yet been well established. The goal of this paper is to construct the sublinear expectation regression and investigate its statistical inference. First, a sublinear expectation linear regression is defined and its identifiability is given. Then, based on the representation theorem of sublinear expectation and the newly defined model, several parameter estimations and model predictions are suggested, the asymptotic normality of estimations and the mini-max property of predictions are obtained. Furthermore, new methods are developed to realize variable selection for high-dimensional model. Finally, simulation studies and a real financial example are carried out to illustrate the new models and methodologies. All notions and methodologies developed are essentially different from classical ones and can be thought of as a foundation for general nonlinear expectation statistics.
