Computer-aided Statistical Inference

Beran 大型数据集的现代统计方法依赖于 高维数据（如傅立叶分析、小波变换或 投影寻踪），平滑（如非参数回归）， 收缩（如Stein估计或岭回归），变量选择 (as在线性回归中），以及这些想法的组合（例如 小波或傅立叶系数的阈值化）。同时，统计学家 已经引入了计算机辅助技术，如交叉验证或 引导，用于评估通过数据恢复的模式的不确定性 分析。该研究项目开发：（a）必要和充分的 Bootstrap分布正确收敛的条件 用于在数据分析中检测引导失败的诊断方法;（B） 调制估计器，其通过自适应地逐渐变细来从噪声中恢复信号 旋转数据加上信号的置信区域，其中心位于 调制估计;（c）所有非参数自举置信集 平均方向（或平均轴）之间的成对旋转差异 方向（或轴向）数据的几个独立样本。 科学和社会测量中的计算机革命创造了 庞大复杂的数据集作为回应，数据分析师设计了计算机- 用于从数据恢复模式的辅助方法。然而，不完整的 数据以及测量误差在测量中引起可能的误差。 得出的结论。最近关于人口普查低估的争议 城市就是一个突出的例子。模式中有多少不确定性 通过复杂的数据分析恢复的吗 统计技术 自1979年以来， 最广泛适用的方法来评估固有的不确定性， 数据分析不幸的是，目前使用的引导方法可能 有时会对不确定性做出误导性的评估。（a）部分 研究项目提供计算机密集型方法来检测和纠正 这样的bootstrap失败。这部分工作有助于联邦 高性能计算的战略领域。项目的第（B）部分开发 从噪声测量中恢复的信号的不确定性评估。 由卫星照相机记录的电子图像就是这种情况的一个例子。 测量.这部分工作提供了统计方法， 在全球变化的联邦战略区域分析卫星数据。部分 (c)该项目为以下分析制定了不确定性评估： 方向和轴向数据集。地震地球物理测量 研究、石油勘探和火山活动的研究是 例如方向和轴向数据。

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.