CAREER: Nonparametric methods in multiple dimensions: shape restrictions, bootstrap and beyond

职业：多维非参数方法：形状限制、引导程序等

• 批准号: 1150435
• 负责人: Bodhisattva Sen
• 金额: $ 40万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1150435&HistoricalAwards=false
• 关键词: CAREER; Nonparametric; methods; multiple; dimensions

This proposal deals with some problems on estimation and inference using nonparametric methods. Nonparametric procedures have become increasingly popular in the theory and practice of statistics in recent times primarily because of their fundamental advantages over parametric methods: greater flexibility and more 'data-driven' features. In this proposal, the investigator studies three core directions of statistical research in this area: (A) Nonparametric function estimation under shape restrictions, (B) Dimension reduction using semi/non-parametric techniques, and (C) Bootstrap based inference in non-standard problems. The main motivation for this research is in developing nonparametric procedures that are completely automated (free from tuning parameters, e.g., smoothing bandwidths) but still flexible enough to incorporate data-driven features. A major part of this proposal deals with nonparametric methods applicable to multivariate data, an area that has received relatively less attention, though often felt to be necessary in performing real data analysis.With the advancement in modern computing facilities and the explosion in collection of large scale data sets, the use of more complicated/intricate statistical procedures involving numerical optimization techniques are becoming increasingly popular. However, a complete theoretical analysis of most of these procedures is still largely unavailable. This research aims at understanding the theoretical and computational aspects of some of these statistical procedures, and quantifying the uncertainties involved in such stochastic optimization problems. The intended applications of the proposed research are diverse, ranging from detecting the advent of global warming, to estimating the radial velocity distribution of stars in a galaxy, to developing inferential techniques for binary choice models (of special interest to econometricians), and would involve collaborations at different levels with statisticians, biostatisticians, epidemiologists, econometricians and astronomers.

该建议涉及使用非参数方法进行估计和推理的一些问题。非参数程序在最近的统计学理论和实践中变得越来越流行，这主要是因为它们的基本优势比参数方法：更大的灵活性和更多的“数据驱动”特征。在该提案中，研究人员研究了该领域统计研究的三个核心方向：（a）在形状限制下的非参数函数估计，（b）使用半/非参数技术降低维度，以及（c）基于自举问题的推论。这项研究的主要动机是开发完全自动化的非参数程序（没有调谐参数，例如平滑带宽），但仍然足够灵活以包含数据驱动的功能。该提案的主要部分涉及适用于多元数据的非参数方法，该方法受到相对较少的关注，尽管通常认为在进行真实数据分析时是必不可少的。随着现代计算设施的进步和大规模数据集合的爆炸爆炸，涉及更复杂/复杂的统计程序的使用，涉及数字技术的越来越多。但是，对大多数这些程序的完整理论分析仍然不可用。这项研究旨在了解其中一些统计程序的理论和计算方面，并量化此类随机优化问题所涉及的不确定性。拟议的研究的预期应用是多种多样的，从检测全球变暖的出现，到估计星系中恒星的径向速度分布到为二元选择模型（对经济学家特别感兴趣）的推理技术发展，并将涉及与统计学家，生物统计学家，生物统计学家，生物统计学家，经济学学家和经济学的合作。