Mathematical Sciences: Aliasing, Approximation and Asymptotics in Some Statistical Models

数学科学：某些统计模型中的混叠、近似和渐近

• 批准号: 8802378
• 负责人: Terence Speed
• 金额: $ 12.81万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802378&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Aliasing; Approximation; Asymptotics

This research examines three classes of statistical models in common use. The first topic is aliasing in models for the covariance function of random processes and arrays. The second topic involves the further use of higher-order cumulants and Edgeworth expansions to study the behaviour of estimators and tests in variance component analysis. The final topic is the method of residual or restricted maximum likelihood estimation of variance and covariance parameters. This research in statistics will impact the areas of spectral analysis, analysis of variance, and the users of the classical random effects and mixed linear models in fields such as agriculture, plant and human genetics, psychology and manufacturing.

本研究考察了常用的三类统计模型。第一个主题是随机过程和随机数组协方差函数模型中的混叠。第二个主题涉及进一步使用高阶累积量和Edgeworth展开式来研究方差成分分析中估计量和检验的行为。最后一个主题是方差和协方差参数的残差或限制最大似然估计方法。这一统计学研究将影响光谱分析、方差分析以及经典随机效应和混合线性模型在农业、植物和人类遗传学、心理学和制造业等领域的使用。