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

本研究考察了三类常用的统计模型。第一个主题是随机过程和阵列的协方差函数的模型中的混叠。第二个主题涉及进一步使用高阶累积量和Edgeworth展开来研究方差分量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约束最大似然估计方法。统计学中的这项研究将影响到光谱分析、方差分析以及农业、植物和人类遗传学、心理学和制造业等领域中经典随机效应和混合线性模型的使用者。

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.