Statistical Models and Methods for Some Applied Problems

该项目的重点是：(1)基于L1数据深度的新概念的多变量方法；(2)将分类器与生物特征测量相结合；(3)具有偏差和不完备性的多变量有序事件时间数据。所有这些都是统计应用和理论的丰富领域，PI在这些领域做出了重要贡献。在(1)中，L1深度的新概念是最近推导出的多变量数据分析工具，包括聚类和稳健回归。这些工具被证明对数据污染是健壮的，渐近有效，并且对高维数据的计算“友好”。这些项目扩展了方法，包括基于深度的聚类验证、信息量可视化以及基于深度相对模型的新概念的多变量线性和非线性回归。在(2)中，基于生物特征数据的分类具有训练数据中对象维度高、类别数多、每类样本数少的特点。最近的研究表明，对于这类问题，分类器的合并可以提高正确分类率。该项目重点研究了基于基准数据的混合分组等级(MGR)组合器的新方法，以改进组成方法以及其他组合方法。该项目进一步开发了MGR型合并器，建立了它们的理论基础，并提供了处理大型数据集所需的计算工具。在(3)中，多变量有序事件-时间数据在观察性研究中很常见，包括流行病学、临床研究、行为研究等。这类数据很难分析，因为它们通常会受到有偏抽样和审查的影响。一个新的多变量非参数框架使得单变量统计方法能够扩展到多维数据。将在非参数和半参数模型中为各种抽样方案开发新的统计方法。渐近(大样本)理论为该方法提供了理论依据。所提出的研究推进了多元统计的几个重要领域。新的模型、方法和算法将被开发用于多变量聚类、稳健的多变量回归、分类器的组合以及有偏的不完整的多变量事件-时间数据的分析。拟议的研究对直接统计领域以外的广泛科学应用有直接影响。例如遗传学研究、生物统计学分类方法、流行病学、临床和行为研究。

The project focuses on: (1) multivariate methods based on the new concept of L1 data-depth, (2) combining classifiers with applications to biometrics measurements, (3) multivariate ordered event-time data with bias and incompleteness. All are rich areas for statistical applications and theory, where the PI's have made important contributions. In (1), the new notion of L1 depth was recently to derive a multivariate data-analytic tools, including clustering and robust regression. These tools were shown to be robust against data contamination, asymptotically efficient, and computationally "friendly" for high dimensional data. The projects extend the methods to include depth-based clustering validation, informative visualization, and multivariate linear- and nonlinear-regression based on a new concept of depth-relative-to-a-model. In (2), classification based on biometrics data is characterized by high dimensionality of objects, large number of classes, and small number of examples per class in the training data. Recent research shows that merging of classifiers can improve correct-classification rate for such problems. The project focuses on the new method of mixed group rank (MGR) combiners which is shown, based on benchmark data, to improve on the constituent as well as on other combination-methods. The project further develops MGR type combiners, establish their theoretical underpinnings, and provide the necessary computational tools to handle large data sets. In (3), multivariate ordered event-time data are common in observational studies, including epidemiology, clinical studies, behavioral studies, and more. Such data are hard to analyze, as they are typically subject to biased-sampling and censoring. A new multivariate nonparametric framework enables the extension of univariate statistical methods to multidimensional data. New statistical methods will be developed in nonparametric and semiparametric models for a variety of sampling schemes. Asymptotic (large sample) theory gives theoretical justification for the methodology.The proposed research advances several important areas in multivariate statistics. New models, methods, and algorithms will be developed for multivariate clustering, robust multivariate regression, combination of classifiers, and the analysis of biased incomplete multivariate event-time data. The proposed research has direct impact on a broad range of scientific applications outside the immediate realm of statistics. Examples include genetics studies, biometrics classification methods, epidemiological, clinical, and behavioral studies.