Collaborative Research: Randomization Inference for Contemporary Problems in Statistics

在信息时代许多新兴应用的推动下，研究人员继续为多重测试和推理中的问题开发新的方法论和伴随的数学理论。对有效方法的进一步动机来自对大型数据集的探索性分析，在这种情况下，“数据窥探”(或“数据挖掘”)的过程往往会导致多重测试和同时推理的挑战。在这类问题中，统计学家面临的挑战是对复杂的数据分析所产生的所有可能的错误进行核算，以便任何由此产生的推论或结论都能可靠地被视为“真实的”，而不是虚假的数据发现或假象。可以肯定地说，可靠的统计方法的数学合理性跟不上对有效新工具的需求。特别是，研究人员开发了随机化测试作为半参数和非参数模型的推断方法，这些模型不依赖于不可验证的假设。在很大程度上，重抽样方法，如Bootstrap和次抽样，在许多问题上是成功的，至少在渐近意义上是成功的，但对许多问题来说，它们并不令人满意。当代统计中这类问题的例子包括“高维”问题和“非常规”问题，其中“维度诅咒”可能导致重抽样方法崩溃，而“非常规”问题的基本数据生成过程中的近似值至少在局部上不一致，则可能导致重抽样方法崩溃。解决的一些具体问题包括托比特回归和具有弱工具的线性回归。此外，重抽样方法不具有精确的有限样本有效性，这可能是排列和秩次检验在许多领域(如医学研究)如此广泛使用的主要原因。研究人员将随机化测试应用于统计学家面临的许多新问题，尽管存在高维、同时推理、未知相关性结构、非高斯性等问题。该方法的一个令人兴奋的特点是，如果构建得当，随机化测试在保证有限样本有效性的假设可能失败的情况下具有良好的稳健性。数学理论的发展以及可行的计算结构。有用的统计方法是分析任何研究或科学实验的关键工具。最近，在DNA微阵列生物技术、计量经济学、金融、教育评估、全球变暖、天文学以及许多其他领域出现的问题的推动下，对高效和可靠的验证性统计方法的需求迅速增长。一般而言，哲学方法是开发既具有有效性稳健性又具有效率稳健性的实用方法，以便随着现代数据分析范围的不断扩大，这些方法可以应用于日益复杂的情况。这项工作的更广泛影响可能是相当大的，因为由此产生的推理工具可以应用于遗传学、生物工程、图像处理和神经成像、临床试验、教育、天文学、金融和计量经济学等不同领域。结果将广泛传播，并尽可能提供新统计工具的公共软件。许多蓬勃发展的应用领域需要新的统计方法，在研究人员的指导下，为年轻学者创造了具有挑战性和激动人心的机会。

The investigators continue the development of new methodology and the accompanying mathematical theory for problems in multiple testing and inference, driven by the many burgeoning applications in the information age. Further motivation for valid methods stems from exploratory analysis of large data sets, where the process of "data snooping" (or "data mining") often leads to challenges of multiple testing and simultaneous inference. In such problems, the statistician is faced with the challenge of accounting for all possible errors resulting from a complex analysis of the data, so that any resulting inferences or conclusions can reliably be viewed as "real" rather than spurious findings or artifacts of the data. It is safe to say that the mathematical justification of sound statistical methods is not keeping pace with the demand for valid new tools. In particular, the investigators develop randomization tests as inferential methods for semi-parametric and nonparametric models that do not rely on unverifiable assumptions. To a great extent, resampling methods, such as the bootstrap and subsampling, are successful in many problems, at least in an asymptotic sense, but for many problems they are unsatisfactory. Examples of such problems in contemporary statistics include "high" dimensional problems, where the "curse of dimensionality" may cause resampling methods to break down, and "non-regular" problems, where a lack of convergence of the approximation that is not at least locally uniform in the underlying data generating process may cause resampling methods to break down. Some specific problems addressed include Tobit regression and linear regression with weak instruments. Moreover, resampling methods do not enjoy exact finite-sample validity, which is perhaps the main reason permutation and rank tests are so commonly used in many fields, such as medical studies. The investigators apply randomization tests to many new problems that statisticians face, despite issues of high dimensionality, simultaneous inference, unknown dependence structures, non-Gaussianity, etc. An exciting feature of the approach is that, properly constructed, randomization tests enjoy good robustness properties in situations where the assumptions guaranteeing finite-sample validity may fail. Mathematical theory is developed as well as feasible computational constructs.Useful statistical methodology is the key tool to analyzing any study or scientific experiment. Recently, the demand for efficient and reliable confirmatory statistical methods has grown rapidly, driven by problems arising in the analysis of DNA microarray biotechnology, econometrics, finance, educational evaluation, global warming, and astronomy, as well as many others. In general, the philosophical approach is to develop practical methods that have both robustness of validity and robustness of efficiency so that they may be applied in increasingly complex situations as the scope of modern data analysis continues to grow. The broader impact of this work is potentially quite large because the resulting inferential tools can be applied to such diverse fields as genetics, bioengineering, image processing and neuroimaging, clinical trials, education, astronomy, finance and econometrics. The results will be widely disseminated, and public software of new statistical tools made accessible whenever possible. The many thriving fields of applications demand new statistical methods, creating challenging and exciting opportunities for young scholars under the direction of the investigators.