首页> 外文OA文献 >Bilinear and Trilinear Regression Models with Structured Covariance Matrices
【2h】

Bilinear and Trilinear Regression Models with Structured Covariance Matrices

机译:具有结构协方差矩阵的双线性和三线性回归模型

代理获取
本网站仅为用户提供外文OA文献查询和代理获取服务,本网站没有原文。下单后我们将采用程序或人工为您竭诚获取高质量的原文,但由于OA文献来源多样且变更频繁,仍可能出现获取不到、文献不完整或与标题不符等情况,如果获取不到我们将提供退款服务。请知悉。

摘要

This thesis focuses on the problem of estimating parameters in bilinear and trilinear regression models in which random errors are normally distributed. In these models the covariance matrix has a Kronecker product structure and some factor matrices may be linearly structured. The interest of considering various structures for the covariance matrices in different statistical models is partly driven by the idea that altering the covariance structure of a parametric model alters the variances of the model’s estimated mean parameters. Firstly, the extended growth curve model with a linearly structured covariance matrix is considered. The main theme is to find explicit estimators for the mean and for the linearly structured covariance matrix. We show how to decompose the residual space, the orthogonal complement to the mean space, into appropriate orthogonal subspaces and how to derive explicit estimators of the covariance matrix from the sum of squared residuals obtained by projecting observations on those subspaces. Also an explicit estimator of the mean is derived and some properties of the proposed estimators are studied. Secondly, we study a bilinear regression model with matrix normally distributed random errors. For those models, the dispersion matrix follows a Kronecker product structure and it can be used, for example, to model data with spatio-temporal relationships. The aim is to estimate the parameters of the model when, in addition, one covariance matrix is assumed to be linearly structured. On the basis of n independent observations from a matrix normal distribution, estimating equations, a flip-flop relation, are established. At last, the models based on normally distributed random third order tensors are studied. These models are useful in analyzing 3-dimensional data arrays. In some studies the analysis is done using the tensor normal model, where the focus is on the estimation of the variance-covariance matrix which has a Kronecker structure. Little attention is paid to the structure of the mean, however, there is a potential to improve the analysis by assuming a structured mean. We formally introduce a 2-fold growth curve model by assuming a trilinear structure for the mean in the tensor normal model and propose an estimation algorithm for parameters. Also some extensions are discussed.
机译:本文的重点是在随机误差为正态分布的双线性和三线性回归模型中估计参数的问题。在这些模型中,协方差矩阵具有Kronecker乘积结构,某些因子矩阵可以线性构造。在不同的统计模型中为协方差矩阵考虑各种结构的兴趣部分是由这样的想法驱使的:更改参数模型的协方差结构会更改模型的估计均值参数的方差。首先,考虑具有线性结构协方差矩阵的扩展生长曲线模型。主要主题是找到均值和线性结构协方差矩阵的显式估计量。我们展示了如何将残差空间(与均值空间正交的补余空间)分解为适当的正交子空间,以及如何从通过对这些子空间进行观测得到的平方残差之和得出协方差矩阵的显式估计。还导出了均值的显式估计量,并研究了所提出的估计量的一些性质。其次,我们研究具有矩阵正态分布随机误差的双线性回归模型。对于那些模型,色散矩阵遵循Kronecker乘积结构,并且可以用于例如以时空关系建模数据。目的是在另外假设一个协方差矩阵是线性结构时估计模型的参数。基于对矩阵正态分布的n个独立观察,建立了估计方程,触发器关系。最后,研究了基于正态分布随机三阶张量的模型。这些模型对于分析3维数据数组很有用。在某些研究中,分析是使用张量法线模型完成的,其中的重点是具有Kronecker结构的方差-协方差矩阵的估计。很少关注均值的结构,但是,有可能通过假设结构化均值来改善分析。我们通过假设张量法线模型中均值的三线性结构来正式引入2倍增长曲线模型,并提出参数估计算法。还讨论了一些扩展。

著录项

  • 作者

    Nzabanita, Joseph;

  • 作者单位
  • 年度 2015
  • 总页数
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类

相似文献

  • 外文文献
  • 中文文献
  • 专利
代理获取

客服邮箱:kefu@zhangqiaokeyan.com

京公网安备:11010802029741号 ICP备案号:京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有
  • 客服微信

  • 服务号