Nonparametric likelihood for dependent data

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。研究者寻求开发有效的非参数似然和重采样方法的依赖或相关的数据结构。该项目特别针对非标准采样设计下空间数据的经验似然方法的发展，研究非平稳时空设置中自举的最佳实现，以及通过旨在削弱数据相关性的数据转换创建新的重采样方法。这项工作旨在为若干相关的数据结构提供有效和准确的统计方法，这些方法适用于不需要对基本数据生成过程进行严格假设的情况。科学调查通常依赖于数据的统计分析，这些数据往往以复杂的方式相互关联。目前的统计方法在很大程度上依赖于选择概率模型来准确地表示数据中的潜在相关性。然而，这种模型选择在实践中可能是困难的，并且从错误的模型中得出的任何推论都可能具有误导性。本研究的目标是开发替代的、无模型的工具，用于与相关数据进行有效的统计推断，这些工具不容易受到模型选择错误的影响，也可以帮助推进环境学、经济学、地质学、天文学等自然遇到相关数据的科学领域的数据推断。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The investigator seeks to develop effective nonparametric likelihood and resampling methods for dependent or correlated data structures. The project particularly targets the development of empirical likelihood methodology for spatial data under nonstandard sampling designs, the investigation of optimal implementation of the bootstrap in non-stationary temporal and spatial settings, and the creation of novel resampling methods through data-transformations aimed at weakening data correlation. This work intends to produce efficient and accurate statistical methodology for several correlated data structures, which are applicable without stringent assumptions on the underlying data-generating process.Scientific investigations commonly rely on the statistical analysis of data, which are often correlated in a complex manner. Current statistical metholodogy depends heavily on selecting probability models to accurately represent the underlying correlation in data. However, such model selection can be difficult in practice and any inference drawn from a mistaken model may be misleading. This research targets developing alternative, model-free tools for valid statistical inference with correlated data, which are not susceptible to errors in model choice and can also help advance data inference in scientific areas such as Environmetrics, Economics, Geology, Astronomy, etc., that naturally encounter correlated data.