Resampling Methods for Temporal and Spatial Processes

【摘要】本课题包括两部分内容：(1)开发一种基于变换的远程依赖数据类引导方法，并研究其性质；(2)针对某些（非标准）空间采样设计下的空间数据，提出了“变概率空间块Bootstrap”和“变概率空间子采样”的类重采样方法。尽管已经提出了许多重采样方法，并证明它们在处理时间序列数据的弱依赖性方面是有效的，但PI的早期工作表明，这些方法在长期依赖性下仅取得有限的成功。由于长期相关数据在许多科学研究中自然而频繁地出现（参见Kuensch， h.r., Beran， J., and Hampel， F. (1993; Annals of Statistics)），因此为此类数据开发有效的重采样方法非常重要。这里提出的基于变换的自举法有一些希望。项目的另一部分处理空间数据。与随机过程只向一个方向发展的时间序列情况不同，具有连续空间指数的过程允许多种发展模式。这导致了空间数据的不同类型（通常是非标准的）渐近。拟议的项目力求为这种情况下的空间数据发展新的重新抽样方法，特别是对于间隔不规则的数据站点。拟议项目的重点是为具有复杂结构的时间序列和空间数据开发适当的重新采样方法，并调查其性质。目前的统计方法主要是基于参数模型，对模型的错误规范很敏感。拟议的研究旨在解决这一需要，并旨在消除目前方法的一些限制。

ABSTRACTThe project consists of two parts, viz., (1) Developing a class bootstrap methods, called the "Transform Based Bootstrap", for long-range dependent data and studying their properties; and (2) Developing a class resampling methods, called the "Varying Probability Spatial Block Bootstrap" and "Varying Probability Spatial Subsampling" for spatial data under some (nonstandard) spatial sampling designs. Although a number of resampling methods have been proposed and shown to be effective in dealing with weak dependence in time series data, an earlier work of the PI reveals that these methods have only limited success under long range dependence. Since long-range dependent data appear naturally and frequently in many scientific studies (cf. Kuensch, H.R., Beran, J., and Hampel, F. (1993; Annals of Statistics)), developing effective resampling methods for such data is important. The transform-based-bootstrap, proposed here, holds some promise. The other part of the project deals with spatial data. Unlike the time-series case where the random process evolves only in one direction, processes with a continuous spatial index allow for more than one evolution pattern. This leads to different types of (often nonstandard) asymptotics for spatial data. The proposed project seeks to develop new resampling methods for spatial data in such cases, particularly for irregularly spaced data-sites.The emphasis of the proposed project is on development of suitable resampling methods for time-series and spatial data having a complex structure and on investigating their properties. Current statistical methodology for dependent data are predominantly parametric model based and are sensitive to model misspecification. The proposed research seeks to address this need and is aimed at removing some of the limitations of the current methodology.