Mathematical Sciences: Assessing Robustness of Inference

数学科学：评估推理的稳健性

• 批准号: 9305547
• 负责人: George Casella
• 金额: --
• 依托单位: Cornell Univ - State: AWDS MADE PRIOR MAY 2010
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9305547&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Assessing; Robustness; Inference

All statistical procedures result in an inference, a statement that is based on both the observed data and the assumed model. Since there are often model assumptions that are difficult (or impossible) to check, it is desirable for inferences to be robust against model assumptions. The inferences that we are most concerned about are post (data accuracy measures for confidence sets and hypothesis tests. Such measures are often derived through decision theoretic or Bayesian arguments, hence are based on assumptions about sampling distributions, loss functions, and prior distributions. Here we want to investigate the performance of accuracy estimators, using both frequentist and Bayesian criteria, as the underlying assumptions are relaxed. We are most interested in procedures constructed from default priors, for these tend to perform well under both frequentist and Bayesian scrutiny. One way that we will address the sampling robustness is to combine the default priors with an empirical likelihood to obtain a (somewhat) automatic inference robust procedure. Robustness of inference will be judged using a variety of criteria such as ranges of posterior probabilities, multiple and distance penalizing loss functions and a new (and promising) theory of dilation of probabilities.

所有的统计过程都会产生一个推论，一个基于观察到的数据和假设模型的陈述。由于经常存在难以（或不可能）检查的模型假设，因此需要对模型假设进行鲁棒性推断。我们最关心的推论是置信度集和假设检验的后数据准确性度量。这些度量通常是通过决策理论或贝叶斯论证得出的，因此是基于对抽样分布、损失函数和先验分布的假设。在这里，我们想研究精度估计器的性能，同时使用频率和贝叶斯准则，因为潜在的假设是宽松的。我们最感兴趣的是由默认先验构造的过程，因为它们往往在频率主义者和贝叶斯审查下都表现良好。我们将解决采样鲁棒性的一种方法是将默认先验与经验似然相结合，以获得（某种程度上）自动推理鲁棒性过程。推理的鲁棒性将使用各种标准来判断，例如后验概率的范围，多重和距离惩罚损失函数以及新的（有前途的）概率扩张理论。