LINEAR METHODS IN STATISTICS

统计学中的线性方法

• 批准号: 3896394
• 负责人: J D MALLEY
• 金额: --
• 依托单位: CENTER FOR INFORMATION TECHNOLOGY
• 依托单位国家: 美国
• 资助国家: 美国
• 起止时间: 至
• 项目状态: 未结题
• 来源: https://reporter.nih.gov/project-details/3896394
• 关键词: artificial intelligence; genetic models; mathematical model; mathematics; model design /development; statistics /biometry

This continuing project will develop new methods in statistics, using algebraic techniques, that have applications for biomedical research. Two areas of major interest are the problems of statistical estimation in the presence of missing data, or data having a known patterned covariance matrix. Recently solutions to both these problems for multinormally distributed data, as well as for counted data (multiway contingency tables) have been obtained. The method solves for the maximum likelihood estimate of the parameter vector, thereby generating estimates that are unbiased as well as asymptotically fully efficient. The technique invokes the Dempster-Laird-Rubin EM algorithm, published in 1977, and Jordan algebras to iteratively solve for the parameter vector. Known properties of Jordan algebras are invoked to guarantee convergence, so that each iteration only uses a matrix multiplication by a single fixed matrix. Applications are in the areas of longitudinal data and repeated measures analysis.

这一持续项目将开发新的统计方法， 代数技术，在生物医学研究中有应用。 主要感兴趣的两个领域是统计估计问题， 存在缺失数据或具有已知模式协方差的数据 矩阵最近解决这两个问题的多正规 分布式数据以及计数数据（多因素列联表） 已经获得。 该方法求解参数的最大似然估计 向量，从而生成无偏的估计值， 渐近完全有效该技术调用 Dempster-Laird-Rubin EM算法，发表于1977年，Jordan代数 迭代求解参数向量。约旦已知房产 代数被调用以保证收敛，因此每次迭代仅 使用矩阵乘以单个固定矩阵。应用程序处于 纵向数据和重复测量分析领域。