A complete sufficient dimension folding theory with novel methods

具有新颖方法的完整的足够维度折叠理论

• 批准号: 1205546
• 负责人: Xiangrong Yin
• 金额: $ 11万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-01 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1205546&HistoricalAwards=false
• 关键词: complete; sufficient; dimension; folding; theory

This proposal is aimed at developing a general formulation and the related methods for sufficient dimension folding where predictors are matrix-/array- valued, and where a specific functional (or parameter) of the conditional distribution is of interest. The past two decades have seen vigorous development of the sufficient dimension reduction methods for vector-valued predictors, and have accrued a striking record of their successful applications. However, many data are matrix-/array-valued, sufficient dimension reduction for vector-valued predictors applying to such data will lose its sufficiency and structure, resulting difficulties in interpretation, and to a large extent these methods treat the conditional distribution as the object of interest, without discriminating between parameter of interest and nuisance parameter. The investigator proposes a new paradigm for sufficient dimension folding for matrix-/array-valued predictors that focuses on a functional of the conditional distribution, which can be any one in a very wide class that covers most of applications. In addition, the investigator proposes to develop a coherent collection of associated techniques for estimation, computation, and asymptotic inference. Recently, high throughput technologies that produce massive amount of complex and high-dimensional data are increasingly prevalent in such diverse areas as business, government administration, environmental studies, machine learning, and bioinformatics. These provide considerable momentum in the Statistics community to develop new theories and methodologies, that are capable of discovering critical evidence from high-dimensional, complex structural and massive data. Sufficient Dimension Folding is a new area of statistical research that arose amidst, and has been propelled by, these new demands. The investigator proposes to formulate the theories and methodologies of sufficient dimension folding so that they can be specifically tailored to target to be estimated. This new paradigm not only synthesizes, broadens, and deepens the recent advances in sufficient dimension folding, but brings the understanding of sufficient dimension folding on a par with classical statistical inference theory, by following the tradition of sufficiency, efficiency, information, parameter of interests, and nuisance parameters, which are the key ideas that had helped to propel classical inference to its maturity.

该提案旨在开发一种通用的公式和相关方法，用于足够的维度折叠，其中预测变量是矩阵/数组值，并且条件分布的特定函数（或参数）是感兴趣的。在过去的二十年里，矢量值预测器的充分降维方法得到了蓬勃发展，并取得了令人瞩目的成功应用记录。然而，许多数据是矩阵/数组值，对应用于此类数据的向量值预测器进行充分的降维将失去其充分性和结构，导致解释困难，并且在很大程度上这些方法将条件分布视为感兴趣的对象，而不区分感兴趣的参数和干扰参数。研究人员提出了一种新的范式，用于矩阵/数组值预测器的足够维度折叠，该范式侧重于条件分布的函数，可以是涵盖大多数应用的非常广泛的类别中的任何一个。此外，研究人员建议开发一套连贯的相关技术，用于估计、计算和渐近推理。 近年来，产生大量复杂和高维数据的高通量技术在商业、政府管理、环境研究、机器学习和生物信息学等不同领域越来越普遍。这些为统计学界发展新的理论和方法提供了巨大的动力，这些理论和方法能够从高维、复杂结构和海量数据中发现关键证据。足够维度折叠是统计研究的一个新领域，它是在这些新需求中产生并受到这些新需求推动的。研究人员建议制定足够维度折叠的理论和方法，以便它们可以针对要估计的目标进行专门定制。这种新范式不仅综合、拓宽和深化了充分维度折叠方面的最新进展，而且遵循充分性、效率、信息、兴趣参数和干扰参数的传统，使对充分维度折叠的理解与经典统计推理理论相提并论，这些传统是帮助经典推理走向成熟的关键思想。