Variable Selection and Related Problems

变量选择及相关问题

• 批准号: 9404408
• 负责人: Edward George
• 金额: $ 7.5万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-09-01 至 1997-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404408&HistoricalAwards=false
• 关键词: Variable; Selection; Related; Problems

The proposed research will develop and evaluate variable selection procedures for multiple regression and related problems. Both the Bayesian and the frequentist points of view will be considered. From the Bayesian perspective, the focus will be on stochastic search variable selection methods which use a hierarchical mixture model to guide variable selection. These methods will include a procedure for fast Bayes variable selection to handle hundreds of variables at once, a procedure for variable selection in generalized linear models, a procedure for variable selection across exchangeable regressions, and a procedure for performing simultaneous variable selection and outlier removal. From the frequentist perspective, the focus will be on a new criterion for evaluating selection criteria called risk inflation. This research will entail the application and generalization of risk inflation to a broad set of model selection problems which includes generalized linear models, order selection procedures for time series models, and change-point selection for estimation in change-point problems. Risk inflation will also be used to gauge the bias of using variable selection procedures in conjunction with heuristic search methods. A new class of variable selection procedures which use adaptive dimensionality penalties will also be developed. One of the main goals of modern statistical methods is to provide statistical models which relate input variables to outputs of interest. For example, such models are used to predict and explain annual crop production in agriculture, interest rates in business and economics, cancer incidence in medicine, and crime rates in sociology. A key component in building such models is the selection of input variables which contain strong predictive and explanatory information. This component is especially important because of the recent proliferation of large databases containing vast numbers of potential input variables. The propos ed research will provide powerful new methods for selecting such input variables for a wide variety of model building situations.

拟议的研究将开发和评估多个回归和相关问题的可变选择程序。 贝叶斯和频繁的观点都将被考虑。 从贝叶斯的角度来看，焦点将放在随机搜索变量选择方法上，该方法使用分层混合模型来指导变量选择。 这些方法将包括一个快速贝叶斯变量选择的过程，以一次处理数百个变量，通用线性模型中可变选择的过程，在可交换回归中进行可变选择的过程，以及执行同时可变选择的过程。 从频繁的角度来看，重点将放在评估称为风险通货膨胀的选择标准的新标准上。 这项研究将需要将风险通货膨胀的应用和概括为广泛的模型选择问题，其中包括通用线性模型，时间序列模型的订单选择程序以及更改点问题中估计的更改点选择。 风险通货膨胀也将用于评估与启发式搜索方法结合使用变量选择程序的偏差。 还将开发一类新的使用自适应维度惩罚的可变选择程序。 现代统计方法的主要目标之一是提供将输入变量与感兴趣的输出相关联的统计模型。 例如，此类模型用于预测和解释农业中的每年农作物生产，商业和经济学的利率，医学癌症发病率以及社会学中的犯罪率。 构建此类模型的关键组成部分是输入变量的选择，这些变量包含强大的预测性和解释性信息。 由于最近包含大量潜在输入变量的大型数据库的扩散，该组件尤其重要。 提案研究将为选择各种模型构建情况选择此类输入变量提供强大的新方法。