Investigations in Robust Analysis of Variance

社会和行为科学中的设计性实验 (and其他领域）通常由技术来处理 方差分析（ANOVA）。 当数据 应用统计学家和其他 从业人员应能够获得可靠的估计， 个别影响，并附有适当的摘要， 可变性的总体度量。 通过大幅增加 适用的可用小样本结果数量有限 对于稳健ANOVA所需的汇总和汇总， 该项目旨在为以下方面提供基础（包括关键表格）： 一个统一的机构的基本推理技术的单向和 双向布局。 对于不满足标准假设的数据（对于 例如，通过包含一些异常观察或通过具有 重尾），需要类似ANOVA的程序， 在广泛的基础分布中。 一些 提出了更一般的线性类的鲁棒程序 模型，也包括回归，可以应用于方差分析 情况下，但在小样本中的表现证据 仍然太有限而不能允许选择优选的技术， 作出必要的组成部分（包括估计影响 以及它们的标准误差，相应的假设检验， 和详细的关键表）， 应用. 这项研究将调查几个 稳健方差分析程序，主要基于M估计， 使用大样本结果和蒙特卡罗建立其 小样本的属性。 这项工作将首先强调 最广泛使用的设计：双向和单向布局。 以前的工作由比克尔，德雷珀，费尔纳，汉佩尔， Hettmansperger，Hoaglin，Huber，约翰逊，Kafadar，Lehmann， 莫斯特勒，洛克，朗切蒂，斯库台，施拉德，斯塔赫尔， Tukey、Yohai和Zombay将提供主要起点。 Mosteller和他的同事提出的研究将 继续从事社会事务司长期支持的工作 多年来，经济科学产生了许多 统计方法的最新发展， 社会科学数据的意义。 主要研究者有一个 在社会科学家和 统计学家，因为这两个技术的显着生产 和更容易获得的教科书材料， 说明了继续发展的方法。

Designed experiments in the social and behavioral sciences (and other fields as well) customarily are handled by techniques associated with the analysis of variance (ANOVA). When the data may not be well behaved, applied statisticians and other practitioners should be able to obtain robust estimates of individual effects, accompanied by suitable summaries and aggregate measures of variability. By adding substantially to the limited number of available small-sample results that apply to the summaries and aggregates required for robust ANOVA, this project aims to provide the basis (including critical tables) for a unified body of basic inferential techniques for one-way and two-way layouts. For data that fail to satisfy the standard assumptions (for example, by containing some anomalous observations or by having heavy tails), ANOVA-like procedures are needed that perform well across a broad range of underlying distributions. A number of proposed robust procedures for the more general class of linear models, which also includes regression, may be applied in ANOVA situations, but evidence on their performance in small samples is still too limited to permit choice of a preferred technique or to make the necessary components (including estimates of effects and their standard errors, corresponding tests of hypotheses, and detailed critical tables) available for statistical applications. The proposed research will investigate several procedures for robust ANOVA, mainly based on M-estimation, using large-sample results and Monte Carlo to establish their properties in small samples. The work will at first emphasize the most widely used designs: two-way and one-way layouts. Previous work by Bickel, Draper, Fellner, Hampel, Hettmansperger, Hoaglin, Huber, Johnson, Kafadar, Lehmann, Mosteller, Rocke, Ronchetti, Rousseeuw, Schrader, Stahel, Tukey, Yohai, and Zamar will provide the main starting points. The research proposed by Mosteller and his associates will continue a line of work long supported by the Division of Social and Economic Science that has over the years produced many of the most innovative developments in statistical methods for making sense of social science data. The Principal Investigator has a most distinguished reputation among both social scientists and statisticians because of remarkable production of both technical and more accessible textbook materials describing and illustrating methods that continue to be developed.