Topics in Heavy Tailed Modeling and Long Range Dependence

重尾建模和远程依赖的主题

• 批准号: 9704982
• 负责人: Sidney Resnick
• 金额: $ 25.65万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-15 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704982&HistoricalAwards=false
• 关键词: Topics; Heavy; Tailed; Modeling; Long

9704982 Resnick Sidney Resnick and Gennady Samorodnitsky will continue a program of research organized around the theme of heavy tailed modeling and its connections to long range dependence. Heavy tailed modeling frequently implies infinite variances and thus departs from Gaussian methods. Broad themes of the research program include parameter estimation and prediction in heavy tailed models, model selection and confirmation, and the interplay between long range dependence and heavy tails. Special attention is given to application areas which include the financial and commodities markets and teletraffic networks such as the World Wide Web. Both probabilistic modeling and statistical issues are emphasized. Statistical issues include coping with changes of methods implied by non-standard data features such as long range dependence, lack of existence of moments and correlations, and dependencies which cannot be captured by linear structures. Probabilistic models will be formulated and studied in an attempt to qualitatively explain observed features of the data. The increasing instrumentation of both financial markets and broadband data networks makes possible the collection of huge quantities of data. Examination of some of the data reveals features that classical statistics and probability models are not used to dealing with and hence, this project has a dual purpose: (a) To develop statistical tools which use the data to more reliably fit models and make predictions; (b) To build probability models which provide qualitative insights into the nature of the system under investigation. For example, modern broadband networks exhibit characteristics much different from what is predicted by classical models. A question which may be answered by this research is, "when is it economically advisable to add service capacity to the network?".

9704982 Resnick Sidney Resnick和Gennady Samorodnitsky将继续围绕重尾建模及其与长期依赖的联系这一主题组织的研究计划。重尾建模通常意味着无穷大的方差，因此与高斯方法不同。该研究计划的广泛主题包括重尾模型中的参数估计和预测、模型的选择和确认，以及长期相关性和重尾之间的相互作用。特别注意应用领域，包括金融和商品市场以及诸如万维网等电信网络。既强调了概率建模，也强调了统计问题。统计问题包括处理非标准数据特征所隐含的方法变化，如长范围相关性、缺少矩和相关性的存在以及线性结构无法捕获的相关性。将制定和研究概率模型，试图定性地解释数据的观测特征。金融市场和宽带数据网络的工具越来越多，使得收集大量数据成为可能。对一些数据的检查揭示了经典统计和概率模型不习惯处理的特点，因此，本项目具有双重目的：(A)开发统计工具，利用数据更可靠地拟合模型并作出预测；(B)建立概率模型，对所调查系统的性质提供定性的见解。例如，现代宽带网络表现出与经典模型所预测的大不相同的特征。这项研究可能回答的一个问题是：“什么时候增加网络的服务能力在经济上是可取的？”