New Developments of Nonlinear Dependent Models, with Applications in Genetics, Finance and the Environment

非线性相关模型的新发展及其在遗传学、金融和环境中的应用

• 批准号: 0804575
• 负责人: Zhengjun Zhang
• 金额: $ 18万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-06-01 至 2012-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0804575&HistoricalAwards=false
• 关键词: New; Developments; Nonlinear; Dependent; Models

High-dimensional and complex data are now collected routinely in the fields of environment, financial markets, and signal and image processing. A major challenge is to find methods to analyze the structure of such data sets, to fit models with desired dependence properties, and to identify and validate patterns. A major goal of the proposal is to make significant methodological and theoretical contributions to the important and challenging low-sample and high-dimension statistical inference problems such as dimension reduction in bio-informatics, and extreme dependence problems arising from environmental, and financial markets. The proposal consists of four important steps. First, the proposal pursues a series of developments of new measures for nonlinear dependencies. The investigator studies the limiting distributions of dependence measures (quotient correlation coefficients) and analyzes asymptotic powers when the dependence structures are specified. In DNA microarray data analysis, the quotient correlation is used to select the best feature subset of genes, and then the selected subset is used to predict classes for all sample data. Second, a tail dependent measure (a tail quotient correlation coefficient) with varying threshold is introduced. This measure is related to the study of statistics of multivariate extremes, and is used to assess asymptotic (in)dependencies in environmental variables. Third, the proposal includes the development of statistical estimation methods for asymptotically (in)dependent multivariate maxima and moving maxima processes. This allows one to efficiently study clustered spatial-temporal extreme observations. Fourth, the proposal studies GARCH(r,s) models with m-dependent residuals.The intellectual merit of the proposal in a first instance stems from an efficient dimension reduction approach using the quotient correlation concept. In DNA microarray data analysis, in which there are thousands of variables (genes) in gene expression profiles, and class prediction is an important problem. It is important to identify subsets of genes to work with, due to the high dimensional feature and small sample size of the data under investigation. The ultimate goal is to select the smallest subset of genes which contribute toward the classifications and predictions. Among existing gene selection methods, it is hard to find one which always performs better than the rest when applying them to different data sets. The proposal specifically aims at finding a solution for this. Beyond methodological merits and specific applications, the proposal also has a considerable broad impact. Throughout applications in diverse fields (like above), extreme risks play an important scientific, societal, as well as (possibly) political role. The dissemination of new statistical tools leading to a better understanding of the occurrence of joint extremes is of great importance. This can be well achieved at the level of new graduate courses, publications in journals aimed at a broad audience and in discussion with scientists from other fields. To name just one potential example where the proposal has great impact, let us consider financial risk management. Due to the establishment of new regulatory-rules for banking solvency (so-called Basel II proposal), banks have to come up (in their analysis of credit risk, for instance) with stress testing procedures which can immediately be formulated in terms of extremal co-movements. Similarly, in multi-line insurance, underwriters have to take care of joint large losses in many different lines of business. It is exactly for these kinds of applications that the proposal yields new tools.

现在，在环境、金融市场、信号和图像处理等领域，经常收集高维和复杂的数据。一个主要的挑战是找到方法来分析这样的数据集的结构，以适应模型所需的依赖性，并识别和验证模式。该提案的一个主要目标是为重要和具有挑战性的低样本和高维统计推断问题（如生物信息学中的降维问题以及环境和金融市场产生的极端依赖问题）做出重要的方法和理论贡献。该提案包括四个重要步骤。首先，该建议追求一系列的发展新措施的非线性依赖。调查研究的依赖措施（商相关系数）的极限分布，并分析渐近权力时，依赖结构指定。在DNA微阵列数据分析中，利用商相关性来选择基因的最佳特征子集，然后利用所选择的子集来预测所有样本数据的类别。其次，引入了一种具有可变阈值的尾相关测度（尾商相关系数）。这一措施涉及到多元极端统计的研究，并用于评估环境变量的渐近（不）依赖性。第三，该提案包括渐近（不）相关的多变量最大值和移动最大值过程的统计估计方法的发展。这使得人们能够有效地研究集群时空极端观测。第四，研究了残差m相依的Gestival（r，s）模型，其理论价值首先来自于利用商相关概念的有效降维方法。在DNA微阵列数据分析中，基因表达谱中的变量（基因）多达数千个，类别预测是一个重要的问题。由于研究数据的高维特征和小样本量，识别基因的子集是很重要的。 最终目标是选择有助于分类和预测的最小基因子集。在现有的基因选择方法中，很难找到一种在应用于不同数据集时总是比其他方法表现更好的方法。该提案的具体目的是为此找到解决办法。 除了方法上的优点和具体应用之外，该建议还具有相当广泛的影响。在不同领域的应用中（如上所述），极端风险发挥着重要的科学，社会以及（可能）政治作用。 传播新的统计工具，从而更好地了解联合极端事件的发生，这一点非常重要。在新的研究生课程、在面向广大读者的期刊上发表文章以及与其他领域的科学家进行讨论时，都可以很好地实现这一目标。仅举一个提案具有重大影响的潜在例子，让我们考虑金融风险管理。由于建立了新的银行偿付能力监管规则（所谓的巴塞尔II提案），银行必须提出（例如，在其信用风险分析中）压力测试程序，这些程序可以立即根据极端的共同运动来制定。同样，在多险种保险中，承保人必须处理许多不同险种的共同巨额损失。正是针对这些类型的应用，该提案产生了新的工具。