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

我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。最近提出的一种微分对数密度逼近，具有许多理想的性质，需要进一步研究。我将把我关于位于矩形、多边形和平行四面体中的随机点之间的距离分布的结果推广到位于多边形金字塔中的随机点，并考虑在运输物流中的某些应用，例如与城际交通和空中加油机定位相关的应用。广义分布的进一步发展应该会导致可靠性分析和质量控制方面的更有效的技术。贝叶斯预测方法将被用来对生物医学领域，特别是统计遗传学中出现的问题进行推断。将已发表的时间序列分布结果推广到一般的ARMA模型也在研究中。我打算探索椭圆等值线分布的另一种结构表示；有前景的应用包括利用厚尾分布创新对时间序列进行建模，以及开发用于模拟涉及椭圆等值线向量的函数的有效替代技术等。我将开发有效的算法来确定奇异椭圆轮廓或复杂随机向量中不定二次型的分布函数。我将在Wolfram的网站上提供与我的几个结果相关的代码。我还在准备关于密度估计和厄米特二次型的专著。最后，我的目标是完成一本关于多元统计分析的教科书，增加关于分类、多变量方差分析和广义线性模型的章节。

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.