Investigations in Robust Analysis of Variance

在社会科学和行为科学（以及其他领域）中设计的实验通常是由与方差分析（ANOVA）相关的技术处理的。当数据可能表现不佳时，应用统计学家和其他从业人员应该能够获得对个别影响的可靠估计，并附有适当的摘要和变异性的总体测量。通过大量增加可用的有限数量的小样本结果，这些结果适用于鲁棒方差分析所需的摘要和聚合，该项目旨在为单向和双向布局的基本推断技术的统一体提供基础（包括关键表）。对于不能满足标准假设的数据（例如，包含一些异常观测值或具有重尾），需要在广泛的潜在分布范围内表现良好的类方差分析程序。许多针对更一般的线性模型（也包括回归）提出的稳健程序可以应用于方差分析情况，但关于它们在小样本中的表现的证据仍然太有限，无法选择首选技术或做出必要的组成部分(包括效果及其标准误差的估计、相应的假设检验、以及可用于统计应用的详细关键表。拟议的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在小样本中建立它们的性质。这项工作将首先强调最广泛使用的设计：双向和单向布局。Bickel、Draper、Fellner、Hampel、Hettmansperger、Hoaglin、Huber、Johnson、Kafadar、Lehmann、Mosteller、Rocke、Ronchetti、Rousseeuw、Schrader、Stahel、Tukey、Yohai和Zamar之前的工作将提供主要的起点。Mosteller和他的同事们提出的这项研究将继续由社会和经济科学部长期支持的一系列工作，这些工作多年来在统计方法方面产生了许多最具创新性的发展，用于理解社会科学数据。首席研究员在社会科学家和统计学家中享有最杰出的声誉，因为他出色地编写了技术和更容易理解的教科书材料，描述和说明了不断发展的方法。

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.