Application of jordan algebra for testing hypotheses about structure of mean vector in model with block compound symmetric covariance structure

@article{Zmyslony2018ApplicationOJ,
  title={Application of jordan algebra for testing hypotheses about structure of mean vector in model with block compound symmetric covariance structure},
  author={R. Zmyslony and I. Zezula and Arkadiusz Kozioł},
  journal={Electronic Journal of Linear Algebra},
  year={2018},
  volume={33},
  pages={41-52}
}
In this article authors derive test for structure of mean vector in model with block compound symmetric covariance structure for two-level multivariate observations. One possible structure is so called structured mean vector when its components remain constant over sites or over time points, so that mean vector is of the form $\boldsymbol{1}_{u}\otimes\boldsymbol{\mu}$ with $\boldsymbol{\mu}=(\mu_1,\mu_2,\ldots,\mu_m)'\in\mathbb{R}^m$. This hypothesis is tested against alternative of… Expand
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References

SHOWING 1-10 OF 21 REFERENCES
Testing the equality of mean vectors for paired doubly multivariate observations in blocked compound symmetric covariance matrix setup
TLDR
A natural extension of the Hotelling's T 2 statistic, the Block T 2 ( B T 2 ) statistic, a convolution of two T 2 's, which uses unbiased estimates of the component matrices of the orthogonally transformed blocked compound symmetric covariance matrix that is present in a data set. Expand
Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure
TLDR
The free-coordinate approach is used to prove that the quadratic estimation of covariance parameters is equivalent to linear estimation with a properly defined inner product in the space of symmetric matrices. Expand
Estimating and Testing a Structured Covariance Matrix for Three-Level Multivariate Data
This article considers an approach to estimating and testing a new Kronecker product covariance structure for three-level (multiple time points (p), multiple sites (u), and multiple responseExpand
Free-coordinate estimation for doubly multivariate data
Abstract The article addresses the best unbiased estimators of the block compound symmetric covariance structure for m −variate observations with equal mean vector over u sites under the assumptionExpand
Testing and Estimation in the Block Compound Symmetry Problem
Known results for testing and estimation problems for patterned means and covariance matrices with explicit linear maximum likelihood estimates are applied to the block compound symmetry problem. NewExpand
Quadratic Subspaces and Completeness
has been to determine conditions under which a complete sufficient statistic exists for a family of multivariate normal distributions. One approach to this problem, first formulated for a completelyExpand
Applied Multivariate Statistical Analysis
(NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.) I. GETTING STARTED. 1. Aspects of Multivariate Analysis. Applications of Multivariate Techniques. TheExpand
Linear Models with Exchangeably Distributed Errors
Abstract A generalization of the general linear model is considered. Let Y i = α + T i y + e i, i = 1, …, n, where the Y i are 1 × p observed random variables, the T i are 1 × (r − 1) constantExpand
The coordinate-free approach to Gauss-Markov estimation
Content.- 1. Justification of the coordinate-free approach.- 2. Vector-spaces.- a) Definition of a vector-space.- b) Inner products and semi-inner products.- c) Bases of a vector-space, orthogonalExpand
On an Algebraic generalization of the quantum mechanical formalism
One of us has shown that the statistical properties of the measurements of a quantum mechanical system assume their simplest form when expressed in terms of a certain hypercomplex algebra which isExpand
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