Fully Nonparametric Models for Random Effects, Order Thresholding, Boostrap Testing, and Applications

信息收集方面的技术进步，以及数学创新与生物、海洋/大气和心理社会科学的日益融合，在跨学科研究背景下创造了大量高度复杂和非常高维的数据集。这些数据的非标准特征包括非正态、复杂的异质性和相依结构、高维、低样本量和不平衡设计。研究人员为这些数据集提出了更现实的统计模型，并为其分析开发了先进的统计方法。本项目有五个具体目标：通过为交叉和嵌套的双向随机和混合效应设计提出完全非参数模型来增强建模备选方案，为每个模型下的共同感兴趣的假设构建统计程序(包括稳健的基于等级的程序)，提出用于降低备选假设的维度和识别信号位置的顺序阈值(基于L统计量的阈值)，提出用于提高测试程序精度的自助式测试方法，以及通过最近开发的基于测试的分类方法探索上述测试程序在分类问题中的应用。所提出的模型和方法在方法上与标准似然方法、非参数和半参数模型以及贝叶斯技术有根本的不同。统计分析是许多昂贵的科学研究的最后阶段，而且往往是最重要的阶段，这一事实具有重要意义。沿海水域中某些污染物的浓度是下降还是上升的趋势？污染物浓度的趋势是自然过程的结果，还是由人类活动造成的？在不同的生物环境下，基因的表达是否不同？哪些基因是造成这种差异的原因？有帮派抵抗教育培训(G.R.E.A.T.)该计划在减少城市地区青少年越轨/非法活动方面是否有效？在使用生化武器的早期检测中，是否有信号(某一症状的频率高于本底)？如果有，它位于哪里？通常，为回答这类问题而收集的数据表现出高度的非标准特征。美国国家海洋和大气局监测海洋环境质量的国家现状和趋势计划的贻贝观察项目收集的数据，就是此类数据所能展示的复杂特征类型的一个很好的例子。由于它们的非标准特征，数据可能无法满足替代模型和方法所要求的规律性条件。在不满足的假设下分析数据可能会导致关于统计上显著的因素和趋势的错误结论，或者可能无法识别现有的信号或受疾病影响的基因。这项提议的目标是根据现实的统计模型制定先进的数据分析方法，并开发用于实施这些方法的软件。

Technological advancements in information gathering, and the increased fusion of mathematical innovation with biological, oceanic/atmospheric, and psychosocial sciences, have created a plethora of highly complex and very high-dimensional data sets in interdisciplinary research contexts. The non-standard features of such data include non-normality, complex heterogeneity and dependence structures, high-dimensionality, low sample sizes and unbalanced designs. The investigator puts forth more realistic statistical models for such data sets and develops advanced statistical methods for their analysis. This project has five specific aims: to enhance the modeling alternatives by proposing fully nonparametric models for crossed and nested two-way random and mixed effects designs, to construct statistical procedures for the common hypotheses of interest under each of these models (including robust rank-based procedures), to propose order thresholding (thresholding based on L-statistics) for reducing the dimensionality of the alternative hypothesis and for identification of the signal location, to propose a bootstrap testing method for improved accuracy of the test procedures, and to explore applications of the aforementioned test procedures to classification problems, through the recently developed test-based classification method. The proposed models and methods are fundamentally different in approach from the standard likelihood methods, the non- and semi-parametric models, and the Bayesian techniques.The significance of this project stems from the fact that statistical analysis is the final, and often the most important, stage of many expensive scientific investigations. Does the concentration of certain contaminants in coastal waters have a decreasing or an increasing trend? Is a trend in the concentration of contaminants a result of natural processes or is it caused by human activity? Are gene expressions different under different biological environments and which genes are responsible for this difference? Has the Gang Resistance Education and Training(G.R.E.A.T.) program been effective in reducing adolescent deviant/illegal activities in urban areas? In early detection of the use of bioweapons, is there a signal (a certain symptom at rates higher than background) and if so where is it located? Typically, the data collected for answering such questions exhibit highly non-standard features. The data being collected by the Mussel Watch Project of NOAA's National Status and Trends program for monitoring marine environmental quality, is a good example of the type of complex features such data can exhibit. Due to their non-standard features, the data may fail to satisfy the regularity conditions that alternative models and methods require. Analyzing data under assumptions that are not satisfied may lead to incorrect conclusions regarding the statistically significant factors and trends, or may fail to identify an existing signal or the genes that are affected by a disease. The objective of this proposal is to develop advanced methods for data analysis based on realistic statistical models, and to develop software for their implementation.