Collaborative Research: Randomization Inference for Contemporary Problems in Statistics

研究人员继续开发新的方法和伴随的数学理论，以解决多重测试和推理问题，在信息时代的许多新兴应用的驱动下。有效方法的进一步动机源于对大型数据集的探索性分析，其中“数据窥探”（或“数据挖掘”）的过程经常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数据的复杂分析所产生的所有可能的错误进行解释，以便任何由此产生的推论或结论都可以可靠地视为“真实的”，而不是虚假的发现或数据的人为产物。可以肯定地说，合理统计方法的数学论证跟不上对有效新工具的需求。特别是，研究人员开发随机化测试作为半参数和非参数模型的推理方法，不依赖于不可验证的假设。在很大程度上，重采样方法，如自举和子采样，在许多问题中是成功的，至少在渐近意义上，但对于许多问题，它们是不令人满意的。当代统计学中此类问题的例子包括“高”维问题，其中“维数诅咒”可能导致重采样方法失效，以及“非规则”问题，其中在底层数据生成过程中缺乏近似的收敛性，至少在局部不均匀，可能导致重采样方法失效。讨论的一些具体问题包括Tobit回归和弱工具线性回归。此外，重新抽样方法不具有精确的有限样本效度，这可能是排列和秩检验在许多领域（如医学研究）如此普遍使用的主要原因。研究人员将随机化检验应用于统计学家面临的许多新问题，尽管存在高维性、同时推理、未知依赖结构、非高斯性等问题。该方法的一个令人兴奋的特点是，在保证有限样本有效性的假设可能失败的情况下，正确构造的随机化检验具有良好的鲁棒性。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，由于DNA微阵列生物技术分析、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，对高效可靠的验证性统计方法的需求迅速增长。一般来说，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，它们可以应用于日益复杂的情况。这项工作的广泛影响可能相当大，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。调查结果将广为散发，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，为年轻学者在研究人员的指导下创造了具有挑战性和令人兴奋的机会。

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.