Computer-intensive Methods for the Statistical Analysis of Dependent Data

该项目涉及到重新采样和次采样的持续发展，因为它们适用于相关数据，即时间序列，随机场和（标记）点过程。研究者的工作转向：(a)放宽依赖数据的计算机密集型方法的渐近有效性的条件（例如，允许非平稳性，慢混合率等）；(b)通过设计一个内置程序来估计有关统计量的收敛速度，使子抽样更加“自动化”；(c)通过Richardson外推等技术和块大小的最佳选择来提高分布估计的准确性；(d)制订适当的重新抽样/次抽样方法，以便在其他数据收集情况下，如在间隔不规则的地点进行测量的情况下，即从标记点过程获得的数据；(e)探索时间序列“局部”重采样的思想。本研究的重点是发展计算机密集的统计推断方法，用于分析相关数据，而不必依赖于不现实或不可验证的模型假设。依赖数据的统计分析在许多不同的科学学科中是至关重要的；因此，该研究具有许多潜在的实际应用价值。例如，考虑复杂制造系统的随机计算机仿真问题，这是工业工程中的一个重要问题；为了评估模拟的收敛性和准确性，对“几乎”平稳时间序列的子抽样方法是最有帮助的。再例如，假设X(t)表示环境测量值，例如在位置t测量的降雨量或臭氧浓度。通常，测量X(t)的t点在空间或地球表面上不规则地分散。发展一种涉及这类数据的统计推断的一般方法是对空间统计，特别是涉及地质、大气和环境数据的研究的重大贡献。

Politis 9703964 This project involves the on-going development of resampling and subsampling as they apply to dependent data, i.e., time series, random fields, and (marked) point processes. The investigator's efforts redirected towards: (a) relaxing the conditions for asymptotic validity of computer-intensive methods for dependent data (e.g., allow for nonstationarity, slow mixing rate, etc.); (b) rendering subsampling more `automatic' by devising a built-in procedure for estimation of the rate of convergence of the statistic in question; (c) improving the accuracy of distribution estimation by techniques such as Richardson extrapolation, and by optimal choice of block size; (d) developing appropriate resampling/subsampling methods in the case of alternative data-collection scenarios as is the case of measurements at irregularly spaced locations, i.e., data from a marked point process; and (e) exploring the idea of `local' resampling for time series. This research focuses on the development of computer-intensive methods of statistical inference for the analysis of dependent data without having to rely on unrealistic or unverifiable model assumptions. The statistical analysis of dependent data is vital in many diverse scientific disciplines; thus this research has potentially many practical applications. For example, consider the problem of stochastic computer simulation of complex manufacturing systems that is an important issue in Industrial Engineering; the methodology of subsampling for `almost' stationary time series is most helpful in order to assess convergence and accuracy of the simulation. For another example, suppose that X(t) denotes an environmental measurement, e.g., rain precipitation or ozone concentration as measured at location t. Typically, the t-points where X(t) is measured are irregularly scattered in space or on the earth's surface. The development of a general methodology for statistical inference involving data of this type is a significant contribution i n spatial statistics and, in particular, studies involving geological, atmospheric, and environmental data.