Nonparametric Likelihood Enhancements for Dependent Data

该项目旨在为相关数据制定准确的统计方法，该方法适用于不需要对数据如何产生的严格假设。当前的统计方法通常依赖于为相关数据指定一个适当的模型，这可能是一项艰巨的任务，而且从错误的模型中得出的任何推论都可能是不可靠的。这项研究的一个直接好处是为统计推断提供了替代的、无模型的工具，这些工具不受模型选择的影响，可以推进环境学、经济学、天文学等科学领域的数据分析，这些领域遇到了不同形式的复杂依赖数据。此外，气候预测与减轻自然灾害和规划社会/经济资源的使用日益相关。研究目标包括开发新的区域气候模式评估，以了解这些模式的尺度差异如何影响气候预报。研究目标是针对不同类型的时空依赖数据结构开发无模型重采样和非参数似然方法。三个主要的研究问题是：(1)研究时间序列的经验似然的最优实现（因为性能以目前未知的方式与调整参数相关）；(2)研究地球物理和环境过程中“尺度”概念的时空重采样方法，并对区域气候模式进行评估；(3)开发基于数据转换的不规则空间观测重采样新方法，提高空间数据推断能力。这种非参数方法可以在温和的分布假设下对依赖结构进行有效的推断和评估，也有助于为模型选择提供信息。

The project aims to develop accurate statistical methodology for correlated data, which applies without stringent assumptions about how data may arise. Current statistical methodology often relies on specifying an adequate model for correlated data, which can be a difficult task, and any inference drawn from a mistaken model can be unreliable. A direct benefit of this research is to provide alternative, model-free tools for statistical inference that are not susceptible to model choice and can advance data analysis in scientific areas such as environmetrics, economics, astronomy, etc., which encounter different forms of complex dependent data. Additionally, climate predictions are increasingly relevant for mitigating natural disasters and planning the use of social/economic resources. Research goals include developing new assessments of regional climate models to understand how scale differences in such models may impact climate forecasts. The research targets development of model-free resampling and nonparametric likelihood methods for different types of dependent data structures, temporally and spatially. Three main research problems are: (1) Investigation of optimal implementations of empirical likelihood for time series (as performance is linked to tuning parameters in currently unknown ways); (2) Study of spatio-temporal resampling methods to assess the concept of "scale" in geophysical and environmental processes, with interest in evaluating regional climate models; (3) Development of new resampling methods for irregularly located spatial observations, based on data-transformations, to advance inference with spatial data. Such nonparametric methods can provide valid inference and assessments of dependence structures under mild distributional assumptions, and such methodology can also be helpful for informing model selection.