Computer-aided Statistical Inference

计算机辅助统计推断

• 批准号: 9530492
• 负责人: Rudolph Beran
• 金额: $ 17.1万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9530492&HistoricalAwards=false
• 关键词: Computer; aided; Statistical; Inference

Beran Modern statistical methods for large data sets rely on rotation of the data in high dimensions (as in Fourier analysis, wavelet transforms, or projection pursuit), on smoothing (as in nonparametric regression), on shrinkage (as in Stein estimation or ridge regression), on variable selection (as in linear regression), and on combinations of these ideas (such as thresholding of wavelet or Fourier coefficients). Concurrently, statisticians have introduced computer-aided techniques, such as cross-validation or the bootstrap, for assessing the uncertainty in patterns recovered though data analyses. This research project develops: (a) necessary and sufficient conditions under which bootstrap distributions converge correctly plus diagnostic methods for detecting bootstrap failure in data analyses; (b) modulation estimators that recover a signal from noise by adaptively tapering the rotated data plus confidence regions for the signal that are centered at the modulation estimators; (c) nonparametric bootstrap confidence sets for all pairwise rotational differences among the mean directions (or mean axes) of several independent samples of directional (or axial) data. The computer revolution in scientific and social measurement has created large, complex data sets. In response, data analysts have devised computer- assisted methods for recovering patterns from data. However, incompleteness of the data as well as measurement errors induce possible errors in the conclusions reached. The recent controversy about Census undercounts in the cities is a prominent example. How much uncertainty is there in patterns recovered through sophisticated data-analyses? The statistical technique called the bootstrap, which relies on fast computers, has grown since 1979 into the most widely applicable method for assessing uncertainties inherent in data-analyses. Unfortunately, bootstrap methods, as currently used, can sometimes give a misleading asse ssment of uncertainty. Part (a) of this research project provides computer-intensive ways to detect and to correct such bootstrap failure. This portion of the work contributes to the Federal Strategic Area of high-performance computing. Part (b) of the project develops uncertainty assessments for signals recovered from noisy measurements. Electronic images recorded by a satellite camera are an instance of such measurements. This portion of the work provides statistical methodology for analyzing satellite data in the Federal Strategic Area of global change. Part (c) of the project develops uncertainty assessments for analyses of directional and axial data sets. Geophysical measurements in earthquake studies, oil exploration, and studies of volcanic activity are examples of such directional and axial data.

大型数据集的现代统计方法依赖于高维数据的旋转（如在傅立叶分析、小波变换或投影追踪中）、平滑（如在非参数回归中）、收缩（如在斯坦估计或岭回归中）、变量选择（如在线性回归中）以及这些思想的组合（如小波或傅立叶系数的阈值）。同时，统计学家引入了计算机辅助技术，如交叉验证或自举法，以评估通过数据分析恢复的模式中的不确定性。本研究项目发展：(a)自举分布正确收敛的充分必要条件，以及在数据分析中检测自举失败的诊断方法；(b)调制估计器，通过自适应地减小旋转数据和以调制估计器为中心的信号置信区域，从噪声中恢复信号；(c)几个独立的方向（或轴向）数据样本的平均方向（或平均轴）之间的所有成对旋转差异的非参数自举置信集。科学和社会测量领域的计算机革命创造了庞大而复杂的数据集。作为回应，数据分析人员设计了计算机辅助方法从数据中恢复模式。然而，由于数据的不完整性和测量误差，得出的结论可能存在误差。最近关于城市人口普查漏报的争议就是一个突出的例子。通过复杂的数据分析恢复的模式有多少不确定性？自1979年以来，依赖于快速计算机的统计技术被称为bootstrap，已发展成为评估数据分析中固有不确定性的最广泛应用的方法。不幸的是，目前使用的自举方法有时会对不确定性给出误导性的错误评估。本研究项目的第(a)部分提供了检测和纠正此类引导故障的计算机密集型方法。工作的这一部分有助于高性能计算的联邦战略领域。该项目的第(b)部分对从噪声测量中恢复的信号进行不确定性评估。卫星照相机记录的电子图像就是这种测量的一个例子。这部分工作为分析全球变化联邦战略领域的卫星数据提供了统计方法。该项目的第(c)部分为分析方向和轴向数据集开发了不确定性评估。地震研究、石油勘探和火山活动研究中的地球物理测量就是这种方向和轴向数据的例子。