Mathematical Sciences: Computer Intensive Methods for the Statistical Analysis of Time Series and Random Fields

这个项目的总体目标是开发时间序列和随机场统计分析的推理方法，不依赖于不现实或不可验证的模型假设。自举重采样或计算机密集型方法提供了获得有效分布近似的可行方法，而对生成数据的随机机制几乎没有假设。但是，为了应用这些现代方法，需要解决许多重要的问题。我们希望解决的主要问题包括：在存在非平稳性的情况下，找到计算机密集型方法（特别是子抽样）渐近有效性的一般条件；块重采样与子采样的高阶比较开发计算效率高和准确的标准误差估计，以及对感兴趣参数的置信区域的相应改进；设计参数的最佳选择，以及实施的实用指南；时间序列拟合优度评估；最后利用随机场数据进行区间估计。时间序列和随机场的统计分析，即表现出序列（时间）或空间依赖性的观测，在许多不同的科学学科中都是至关重要的，在物理学、工程学、声学、地质统计学、地球物理学、医学、计量经济学、生态学、林业、地震学等领域都有应用。该项目的总体目标是开发时间序列和随机场背景下的统计推断方法，这些方法不依赖于不切实际或无法验证的模型假设。将采取的主要方法是利用和改进自举法和其他计算机密集型技术，这些技术迄今已得到广泛发展，并已证明在独立观测的背景下非常有用。

Politis The general goal of this project is to develop methods of inference for the statistical analysis of time series and random fields that do not rely on unrealistic or unverifiable model assumptions. Bootstrap resampling or computer-intensive methods offer viable approaches to obtaining valid distributional approximations while assuming very little about the stochastic mechanism generating the data. However, many important questions need to be addressed in order for these modern approaches to be applied. The main issues we wish to tackle include the following: finding general conditions for asymptotic validity of computer-intensive methods, especially subsampling, in the presence of nonstationarity; higher-order comparison of block-resampling and subsampling; developing computationally efficient and accurate estimates of standard error, and the corresponding improvement on confidence regions for parameters of interest; optimal choice of design parameters, as well as practical guidelines for implementation; assessing goodness of fit in time series settings; and finally interval estimation with random field data. The statistical analysis of time series and random fields, i.e., observations that exhibit serial (temporal) or spatial dependence, is vital in many diverse scientific disciplines, with applications in the fields of physics, engineering, acoustics, geostatistics, geophysics, medicine, econometrics, ecology, forestry, seismology, and others. The general goal of this project is to develop methods of statistical inference in the context of time series and random fields that do not rely on unrealistic or unverifiable model assumptions. The main approach that will be pursued is the utilization and refinement of the bootstrap and other computer-intensive techniques, which so far have been developed extensively and have been proven very useful in the setting of independent observations.