Mathematical Sciences: Some Topics in Generalized RegressionModels

数学科学：广义回归模型中的一些主题

• 批准号: 9202857
• 负责人: Donald Pierce
• 金额: $ 18万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1996-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9202857&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Topics; Generalized

For generalized linear models, including those for survival analysis, improved asymptotic methods based on saddlepoint and related methods will be developed and evaluated. These improve- ments are a natural extension of the asymptotic methods ordinari- ly used for generalized linear models and should come into routine use to verify or to improve on application of standard methods. Aside from practical import, these developments provide insight into the basic nature of asymptotic methods particularly in regard to the effects of nuisance parameters. Closely related Laplace approximations will also be developed for likelihood calculations in generalized mixed linear models involving additional random effects in linear predictors. Statistical regression models relate a response variable to a set of explanatory variables and factors or attributes. A major development in statistics during the past 15 years has been the expansion of classical regression modeling to a much broader field of applications often involving more complicated dependen- cies on the explanatory variables and factors. The aim of this project is to continue the development of this broader theory for generalized regression modeling, emphasizing two directions: first, improvement on necessary approximations in the analysis calculations and second, allowance for still more general dependencies reflected in the variability of the data.

对于广义线性模型，包括用于生存分析的线性模型，将开发和评估基于鞍点和相关方法的改进的渐近方法。 这些改进是用于通用线性模型的渐近方法的自然扩展，应常规使用以验证或改善标准方法的应用。 除了实用进口外，这些发展还提供了对渐近方法的基本本质的见解，尤其是在滋扰参数的影响方面。 在涉及线性预测指标中其他随机效应的广义混合线性模型中，还将开发与紧密相关的拉普拉斯近似值，以进行可能计算。 统计回归模型将响应变量与一组解释变量和因素或属性联系起来。 在过去15年中，统计数据的重大发展是将经典回归建模扩展到更广泛的应用领域，通常涉及对解释变量和因素的更为复杂的依赖。 该项目的目的是继续开发这种更广泛的回归建模理论，强调了两个方向：首先，在分析计算中对必要的近似值进行改进，其次，在数据变异性中反映出更普遍的依赖性的津贴。