Advances in distribution theory with applications to transportation logistics and statiscal genesis

分配理论的进展及其在运输物流和统计生成中的应用

• 批准号: 8666-2009
• 负责人: Provost, Serge
• 金额: $ 1.17万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=497345
• 关键词: Advances; distribution; theory; applications; transportation

I am planning to develop efficient semiparametric approaches to univariate and multivariate regression and density estimation and to study related convergence issues. A recently proposed differentiated logdensity approximant, which turns out to possess numerous desirable properties, requires further investigation. I shall extend my results on the distribution of the distance between random points located in rectangles, polygons and parallelepipeds to random points located in polygonal pyramids, and consider certain applications to transportation logistics, such as those associated with intercity traffic and the positioning of airtankers. Further developments on generalized distributions should lead to more efficient techniques in reliability analysis and quality control. The Bayesian predictive approach will be used to make inferences in connection with problems arising in the biomedical fields, and in particular, in statistical genetics. Extensions of the published distributional results in Time Series to general ARMA models are also being investigated. I intend to explore an alternative structural representation of elliptically contoured distributions; promising applications include the modelling of time series with thick-tailed distributed innovations as well as the development of efficient alternative techniques for simulating functions involving elliptically contoured vectors, among others. I shall develop efficient algorithms for determining the distribution function of indefinite quadratic forms in singular elliptically contoured or complex random vectors. I shall make the code associated with several of my results available on Wolfram's website. I am also preparing monographs on density estimation and Hermitian quadratic forms. Finally, I am aiming to complete a textbook on multivariate statistical analysis with the addition of chapters on classification, multivariate analysis of variance and generalized linear models.

我正计划开发有效的半参数方法来进行单变量和多变量回归和密度估计，并研究相关的收敛问题。最近提出的分化对数密度的近似值（事实证明具有许多理想的特性）需要进一步研究。我应将位于矩形，多边形和并行剥削的随机点之间的距离分布扩展到位于多边形金字塔中的随机点，并考虑在运输物流上的某些应用，例如与城市间流量和空中坦克的位置相关的应用。关于广义分布的进一步发展应导致可靠性分析和质量控制方面的更有效的技术。贝叶斯预测方法将用于与生物医学领域（尤其是统计遗传学）出现的问题有关的推论。也正在研究已发表的分配结果的扩展时间序列到一般ARMA模型。我打算探索椭圆形轮廓分布的替代结构表示；有希望的应用包括具有厚尾分布创新的时间序列的建模，以及开发有效的替代技术，用于模拟涉及椭圆轮廓向量的功能等。我将开发有效的算法，以确定在椭圆形的椭圆形轮廓或复杂随机矢量中不确定二次形式的分布功能。我将使与Wolfram网站上的几个结果相关联。我还在准备密度估计和赫米尔二次形式的专着。最后，我的目标是完成有关多元统计分析的教科书，并增加了有关分类，方差和广义线性模型的多元分析的章节。