Exact inequalities and limit theorems for Rademacher and self-normalized sums, and related statistics
Rademacher 和自归一化和的精确不等式和极限定理以及相关统计
基本信息
- 批准号:0805946
- 负责人:
- 金额:$ 15万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2008
- 资助国家:美国
- 起止时间:2008-08-01 至 2011-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The main objectives of the project are as follows: * Prove the longstanding conjecture on the best constant factor in the Rademacher-Gaussian tail comparison. * Prove another longstanding conjecture, on the asymptotic domination of the Rademacher tail by the Gaussian one. * Consider also the ``asymmetric'' case. * Extend to the case of moderate deviations the result due to Shao et al. on the saddle-point approximation to large-deviation probabilities of a self-normalized sum of independent random variables. * Obtain limit theorems, including Berry-Esseen-type bounds and Cramer-type large-deviation asymptotics, for Pearson's product-moment sample correlation coefficient and a number of similar and more general statistics. Thus, the investigator aims to solve longstanding and difficult problems of probability theory and mathematical statistics. The first two of them concern some of the most important properties of such a classical and fundamental object as the Rademacher sums, whose distributions play the role of the extreme points of the set of the distributions of sums (and self-normalized sums) of any independent symmetric random variables. Extensions to the ``asymmetric'' case will also be considered. Closely related are other main objectives of the project, concerning limit theorems for self-normalized sums (or, equivalently, for Student's statistic). The main impact will be in significantly better understanding of important properties of some of the most fundamental objects in probability theory and mathematical statistics. The successful completion of the project will also result in novel and important applications to such classical objects in statistics as Student's test and Pearson's correlation test, which are some of the very few hypotheses tests used most broadly in sciences and engineering. While there are great difficulties to overcome, it appears that the attainment of these objectives is within reach, given a number of advances already made by the investigator and his rather unique expertise in various areas of probability and statistics, as well as his demonstrated abilities to identify and solve difficult and longstanding problems and also to work effectively in a wide and highly diverse range of fields, including mechanical engineering, biology, operations research and combinatorics, and geometry and physics. Efforts will be made to disseminate results, not only via publication in wide-circulation journals, but also via news networks (stories on the investigator's work on evolution modeling and the Eiffel tower shape modeling have already been broadcast around the world by the United Press International and other news agencies). A number of graduate students will be involved into the project; efforts will be made to recruit from underrepresented minorities.
该项目的主要目标如下:*证明了Rademacher-Gaussian尾部比较中关于最佳常数因子的长期猜想。*证明另一个长期存在的猜想,关于Rademacher尾被高斯尾渐近支配。再考虑一下“不对称”的情况。*将Shao等人关于独立随机变量自归一化和的大偏差概率的鞍点近似的结果推广到中等偏差的情况。*获得Pearson积矩样本相关系数的极限定理,包括berry - esseen型边界和cramer型大偏差渐近性,以及一些类似的更一般的统计量。因此,研究者的目标是解决长期和困难的问题,概率论和数理统计。它们中的前两个涉及Rademacher和这类经典和基本对象的一些最重要的性质,Rademacher和的分布充当任意独立对称随机变量的和(和自归一化和)分布集合的极值点的作用。还将考虑“不对称”情况的扩展。密切相关的是项目的其他主要目标,关于自规格化和的极限定理(或等价地,对于学生的统计)。其主要影响将是对概率论和数理统计中一些最基本对象的重要性质有更好的理解。该项目的成功完成还将导致对诸如学生检验和皮尔逊相关检验等统计学经典对象的新颖和重要应用,这是在科学和工程中最广泛使用的极少数假设检验中的一些。虽然有很大的困难需要克服,但鉴于研究者已经取得的一些进展,以及他在概率和统计各个领域的相当独特的专业知识,以及他在识别和解决困难和长期存在的问题以及在广泛和高度多样化的领域有效工作的能力,这些目标的实现似乎是可以实现的,包括机械工程,生物学,运筹学和组合学,几何学和物理学。将努力传播研究结果,不仅通过在发行量很大的期刊上发表,而且还通过新闻网络传播(合众国际社和其他新闻机构已经向全世界广播了关于研究者在进化模型和埃菲尔铁塔形状模型方面的工作)。一些研究生将参与该项目;将努力从代表性不足的少数民族中招聘。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Iosif Pinelis其他文献
On the Minimal Number of Even Submatrices of 0-1 Matrices
- DOI:
10.1023/a:1027346125086 - 发表时间:
1996-01-01 - 期刊:
- 影响因子:1.200
- 作者:
Iosif Pinelis - 通讯作者:
Iosif Pinelis
A characterization of the convexity of cyclic polygons in terms of the central angles
- DOI:
10.1007/s00022-007-1799-9 - 发表时间:
2008-01-25 - 期刊:
- 影响因子:0.500
- 作者:
Iosif Pinelis - 通讯作者:
Iosif Pinelis
Measure extension by local approximation
- DOI:
10.1007/s11117-017-0507-8 - 发表时间:
2017-06-14 - 期刊:
- 影响因子:0.900
- 作者:
Iosif Pinelis - 通讯作者:
Iosif Pinelis
Nonnegative sum-symmetric matrices and optimal-score partitions
- DOI:
10.1007/s11117-019-00692-2 - 发表时间:
2019-07-13 - 期刊:
- 影响因子:0.900
- 作者:
Iosif Pinelis - 通讯作者:
Iosif Pinelis
An alternative to the Euler–Maclaurin summation formula: approximating sums by integrals only
- DOI:
10.1007/s00211-018-0978-y - 发表时间:
2018-06-28 - 期刊:
- 影响因子:2.200
- 作者:
Iosif Pinelis - 通讯作者:
Iosif Pinelis
Iosif Pinelis的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
相似海外基金
Rural Co-Design and Collaboration: Maximising Rural Community Assets to Reduce Place-Based Health Inequalities
农村共同设计与协作:最大化农村社区资产以减少基于地点的健康不平等
- 批准号:
AH/Z505559/1 - 财政年份:2024
- 资助金额:
$ 15万 - 项目类别:
Research Grant
Uncovering Mechanisms of Racial Inequalities in ADRD: Psychosocial Risk and Resilience Factors for White Matter Integrity
揭示 ADRD 中种族不平等的机制:心理社会风险和白质完整性的弹性因素
- 批准号:
10676358 - 财政年份:2024
- 资助金额:
$ 15万 - 项目类别:
What are the implications of health inequalities such as parental education and household income in BAME 11-16 year old's mental health in Wales
父母教育和家庭收入等健康不平等对威尔士 BAME 11-16 岁心理健康有何影响
- 批准号:
2875399 - 财政年份:2024
- 资助金额:
$ 15万 - 项目类别:
Studentship
Analysing Earnings from Creative Education and Creative Work: Decomposing University, Industry and Social Inequalities.
分析创意教育和创意工作的收入:分解大学、工业和社会不平等。
- 批准号:
ES/Z502455/1 - 财政年份:2024
- 资助金额:
$ 15万 - 项目类别:
Fellowship
Bridging the Gender Data Gap: Using Census Data to Understand Gender Inequalities Across the UK
缩小性别数据差距:利用人口普查数据了解英国各地的性别不平等
- 批准号:
ES/Z502753/1 - 财政年份:2024
- 资助金额:
$ 15万 - 项目类别:
Research Grant
National Partnership to tackle Health Inequalities in Coastal Communities
国家伙伴关系解决沿海社区的健康不平等问题
- 批准号:
AH/Z505419/1 - 财政年份:2024
- 资助金额:
$ 15万 - 项目类别:
Research Grant
ReHousIn - Contextualized pathways to reduce housing inequalities in the green and digital transition
ReHousIn - 减少绿色和数字转型中住房不平等的情境化途径
- 批准号:
10092240 - 财政年份:2024
- 资助金额:
$ 15万 - 项目类别:
EU-Funded
Making Every Community Asset Count: Improving Health and Reducing Inequalities for People Experiencing Homelessness
让每一项社区资产发挥作用:改善无家可归者的健康并减少不平等
- 批准号:
AH/Z505389/1 - 财政年份:2024
- 资助金额:
$ 15万 - 项目类别:
Research Grant
Tackling Health Inequalities with and for the Deaf BSL-Using Communities in Wales
与威尔士使用 BSL 的聋人社区一起解决健康不平等问题
- 批准号:
AH/Z505432/1 - 财政年份:2024
- 资助金额:
$ 15万 - 项目类别:
Research Grant
The Abundance Project: Enhancing Cultural & Green Inclusion in Social Prescribing in Southwest London to Address Ethnic Inequalities in Mental Health
丰富项目:增强文化
- 批准号:
AH/Z505481/1 - 财政年份:2024
- 资助金额:
$ 15万 - 项目类别:
Research Grant