Statistical inference of the eigenspace components of a two-dimensional, symmetric rank-two random tensor
Statistical inference of the eigenspace components of a two-dimensional, symmetric rank-two random tensor
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DOI：
10.1007/s00190-004-0405-2
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发表时间：
2004-12
影响因子：
4.4
通讯作者：
Jianqing Cai;E. Grafarend;B. Schaffrin
中科院分区：
文献类型：
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作者：
Jianqing Cai;E. Grafarend;B. Schaffrin
特征空间分量(即主分量和主方向)在对称二阶随机张量的验证中起着关键作用，例如对于应变和应力。他们对地震区的变形和应力模式、板块构造和冰川均衡调整(冰后反弹)进行了分类。假定应变或应力张量已直接观测到或由其他测量间接确定。根据测量公理，这种对称的二阶张量被认为是随机的。为了进行统计推断，随机张量被假定为张量值的高斯-拉普拉斯正态分布。特征空间综合通过一个非线性向量值函数将特征空间元素与观测值联系起来，从而建立了一种特殊的非线性多变量高斯-马尔可夫模型。对于其线性化形式，成功地构造了特征空间元素的最佳线性一致无偏估计(BLUUE)及其方差-协方差矩阵的最佳不变二次一致无偏估计(BIQUUE)。相关的线性假设检验记录了基于真实测量配置的特征值和特征方向的大的置信度区域。它们导致在处理有关拉伸和收缩以及主应力方向的数据时发出警告声明。
The eigenspace components (i.e. principal components and principal directions) play a key role in the validation of a symmetric rank-two random tensor, e.g. for strain and stress. They classify deformation and stress patterns in earthquake regions, plate tectonics and glacial isostatic adjustment (postglacial rebound). It is assumed that the strain or stress tensor has been directly observed or indirectly determined by other measurements. According to the Measurement Axiom, such a symmetric rank-two tensor is considered random. For its statistical inference, the random tensor is assumed to be tensor-valued Gauss–Laplace normally distributed. The eigenspace synthesis relates the eigenspace elements to the observations by means of a nonlinear vector-valued function, thus establishing a special nonlinear multivariate Gauss–Markov model. For its linearized form, the best linear uniformly unbiased estimation (BLUUE) of the eigenspace elements and the best invariant quadratic uniformly unbiased estimate (BIQUUE) of its variance–covariance matrix have been successfully constructed. The related linear hypothesis test has documented large confidence regions for both eigenvalues and eigendirections based upon real measurement configurations. They lead to a statement of caution when dealing with data concerning extension and contraction, as well as the orientation of principal stresses.