Computer-intensive Methods for the Statistical Analysis of Dependent Data

罗马诺9704487 该项目涉及到应用于相关数据的重新采样和二次采样的持续发展，即，时间序列、随机场和（标记的）点过程。研究者的努力方向是：（a）放宽计算机密集型方法对依赖数据的渐近有效性条件（例如，允许非平稳性、慢混合速率等）; (b)（c）通过Richardson外推等技术和通过块大小的最佳选择提高分布估计的准确性;（d）在其他数据收集设想情况下，制定适当的再抽样/二次抽样方法（例如在不规则间隔位置处测量的情况下，即，（e）探讨“局部”恢复的概念 时间序列。 该项目涉及开发计算机密集型统计推断方法，用于分析相关数据，而不必依赖不切实际或无法核实的模型假设。 相关数据的统计分析在许多不同的科学学科中至关重要，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;对于“几乎”平稳时间序列的子采样方法最有助于评估模拟的收敛性和准确性。对于另一个示例，假设X（t）表示环境测量，例如在位置t处测量的降雨量或臭氧浓度。 通常，测量X（t）的t点不规则地散布在空间或地球表面上。 涉及这类数据的统计推断的一般方法的发展是空间统计学的一个重要贡献，特别是涉及环境数据的研究。

Romano 9704487 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 are directed 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 (e.g. in 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 project involves 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 signif icant contribution in spatial statistics and, in particular, studies involving environmental data.