Multiple Problems in Multiple Testing and Simultaneous Inference

研究者为多重测试和同时推理问题开发了新的方法和理论。处理多重性的经典方法是要求决策规则控制家族错误率，即拒绝至少一个真实零假设的概率。但是，当测试的数量很大时，对家族误差率的控制是如此严格，以至于其他假设几乎没有机会被发现。因此，错误发现率等错误控制措施得到了广泛的应用。对于每一种误差控制措施，都希望在最弱的假设条件下构造出显示误差控制的程序。重采样方法为获得有效的分布近似提供了可行的方法，而对产生数据的随机机制的假设很少。虽然开发了许多新方法，但仍有许多问题有待研究。一些技术挑战包括：随样本量和测试数量增长的渐近性；近似误差的阶数；近似均匀性；最优性理论;方向错误。相关问题也进行了研究，例如跨多个测量的生物等效性的统计评估，随机优势的检验，以及部分确定的计量经济模型的推断。实际上，任何科学实验都是为了回答有关被调查过程的问题，这些问题通常可以正式转化为一组假设。唯一的例外是只考虑一个假设。例如，在临床试验中，即使是单一治疗也可能使用多个结果测量、多个时间点、多个剂量和多个亚组进行评估。此外，由于“数据窥探”（或“数据挖掘”）的影响，也会产生额外的假设。统计学家面临的挑战是解释复杂数据分析所导致的所有可能的错误，这样任何推论或有趣的结论都可以被可靠地视为真实的结构，而不是随机数据的人工制品。一般来说，哲学方法是开发实用方法，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。例如，目前的生物技术和基因组学方法产生了DNA微阵列实验，其中必须同时分析细胞中数千个基因的表达水平。许多新兴的应用领域需要新的统计方法，为PI指导下的年轻学者创造了具有挑战性和令人兴奋的机会。

The investigator develops new methods and theory for problems in multiple testing and simultaneous inference. The classical approach to dealing with multiplicity is to require decision rules that control the familywise error rate, the probability of rejecting at least one true null hypothesis. But when the number of tests is large, control of the familywise error rate is so stringent that alternative hypotheses have little chance of being detected. In response, the false discovery rate and other measures of error control have gained wide use. For each measure of error control, it is desired to construct procedures that exhibit error control under the weakest possible assumptions. Resampling methods offer viable approaches to obtaining valid distributional approximations while assuming very little about the stochastic mechanism generating the data. While many new methods have been developed, many more questions remain and are studied. Some of the technical challenges include: asymptotics that grow with both sample size and number of tests; orders of error in approximation; uniformity in approximation; optimality theory; direction errors. Related problems are also studied, such as the statistical evaluation of bioequivalence across multiple measures, testing for stochastic dominance, and inference for partially identified econometric models.Virtually any scientific experiment sets out to answer questions about the process under investigation, which often can be translated formally into a set of hypotheses. It is the exception that a single hypothesis is considered. For example, in clinical trials, even a single treatment may be evaluated using multiple outcome measures, multiple time points, multiple doses, and multiple subgroups. Moreover, due to effects of ``data snooping'' (or ``data mining''), additional hypotheses arise as well. The statistician is then faced with the challenge of accounting for all possible errors resulting from a complex data analysis, so that any resulting inferences or interesting conclusions can reliably be viewed as real structure rather than artifacts of random data. In general, the philosophical approach is the development of practical methods that 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. For example, current methods in biotechnology and genomics generate DNA microarray experiments, where expression levels in cells for thousands of genes must be analyzed simultaneously. The many burgeoning fields of applications demand new statistical methods, creating challenging and exciting opportunities for young scholars under the direction of the PI.