Mathematical Sciences: Projective Score Methods and Approximate Conditional Inference

数学科学：投影评分方法和近似条件推理

• 批准号: 9404150
• 负责人: Richard Waterman
• 金额: --
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404150&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Projective; Score; Methods

A common theme to the areas of research described in this proposal is the presence of nuisance parameters and the necessity of removing an estimation bias in the parameter of interest, induced by the estimation of the nuisance parameters. The reason why the bias must be removed is that it may lead to inconsistency in the maximum likelihood estimator of the parameter of interest. The projects all use a projective approach to modify the score function for the parameter of interest, so that the bias attributable to the estimation of the nuisance parameter is reduced. The benefits of reducing bias will transfer to more accurate parameter estimates, confidence intervals with better coverage rates and test statistics that for small sample sizes have distributions "closer" to their asymptotic limiting distributions. We live in an age where information, that is data, is abundant. Our statistical understanding of this data arises from making accurate models. The large data sets that we have at hand show that simple models rarely fit the data well, and so we are led to consider more complex models with many unknowns. The proposed research will address the practical implementation and interpretative issues involved with these rich statistical models involving many variables.

一个共同的主题，在这个建议中所描述的研究领域是滋扰参数的存在和必要性，消除估计偏差的参数的兴趣，引起的滋扰参数的估计。必须消除偏倚的原因是它可能导致感兴趣参数的最大似然估计量的不一致。所有项目都使用投影方法来修改感兴趣的参数的评分函数，从而减少了由于估计滋扰参数而导致的偏差。减少偏差的好处将转移到更准确的参数估计、具有更好覆盖率的置信区间以及对于小样本量具有“更接近”其渐进极限分布的分布的检验统计量。我们生活在一个信息，也就是数据丰富的时代。我们对这些数据的统计理解来自于建立准确的模型。我们手头的大型数据集表明，简单的模型很少能很好地拟合数据，因此我们不得不考虑具有许多未知数的更复杂的模型。拟议的研究将解决实际实施和解释问题，涉及这些丰富的统计模型，涉及许多变量。