Computer-intensive Methods for the Statistical Analysis of Dependent Data

POLITIS 9703964该项目涉及对相关数据，即时间序列、随机场和(标记的)点过程应用重采样和次采样的持续发展。调查者的努力转向：(A)放宽相关数据的计算机密集方法的渐近有效性的条件(例如，允许非平稳性、混合速度慢等)；(B)通过设计估计有关统计量的收敛速度的内置程序，使二次抽样更加“自动化”；(C)通过诸如Richardson外推等技术和通过最佳选择区块大小来提高分布估计的精度；(D)在其他数据收集方案的情况下，制定适当的重采样/次采样方法，如在不规则间隔位置进行测量的情况，即来自标记点过程的数据；和(E)探讨对时间序列进行“本地”重采样的想法。这项研究的重点是开发计算机密集的统计推断方法，用于分析相关数据，而不必依赖不现实或不可验证的模型假设。相关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，这项研究具有潜在的许多实际应用。例如，考虑复杂制造系统的随机计算机模拟问题，这是工业工程中的一个重要问题；对几乎平稳的时间序列进行次抽样的方法对于评估模拟的收敛和精度是最有帮助的。再例如，假设X(T)表示环境测量，例如在位置t处测量的降雨或臭氧浓度。通常，测量X(T)的t点不规则地散布在空间或地球表面上。发展一种涉及这类数据的统计推断的通用方法是对空间统计，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.