Nonparametric Likelihood Enhancements for Dependent Data

该项目旨在为相关数据开发准确的统计方法，该方法无需对数据如何产生做出严格的假设。目前的统计方法往往依赖于为相关数据指定适当的模型，这可能是一项困难的任务，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不受模型选择影响的替代的、无模型的工具，并可以促进环境计量学、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相关数据。此外，气候预测对于减轻自然灾害和规划社会/经济资源的使用越来越重要。研究目标包括开发新的区域气候模型评估，以了解此类模型的规模差异可能如何影响气候预测。这项研究的目标是为不同类型的相关数据结构，在时间和空间上开发无模型重采样和非参数似然方法。三个主要研究问题是：(1)研究最佳实施时间序列的经验似然性(因为性能与调谐参数的方式目前尚不清楚)；(2)研究时空重采样方法，以评估地球物理和环境过程中的“尺度”概念，并对区域气候模型进行评估；(3)在数据转换的基础上，为位置不规则的空间观测制定新的重采样方法，以推进对空间数据的推断。这种非参数方法可以在温和的分布假设下提供对相关性结构的有效推断和评估，并且这种方法也有助于模型的选择。

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.