Gaussian and robust Kronecker product covariance estimation: Existence and uniqueness
نویسندگان
چکیده
منابع مشابه
Gaussian and robust Kronecker product covariance estimation: Existence and uniqueness
We study the Gaussian and robust covariance estimation, assuming the true covariance matrix to be a Kronecker product of two lower dimensional square matrices. In both settings we define the estimators as solutions to the constrained maximum likelihood programs. In the robust case, we consider Tyler’s estimator defined as the maximum likelihood estimator of a certain distribution on a sphere. W...
متن کاملModels with a Kronecker Product Covariance Structure: Estimation and Testing
In this article we consider a pq-dimensional random vector x distributed normally with mean vector θ and the covariance matrix Λ, assumed to be positive definite. On the basis of N independent observations on the random vector x, we wish to estimate parameters and test the hypothesis H: Λ = Ψ ⊗Σ, where Ψ = (ψij) : q × q and Σ = (σij) : p × p, and Λ = (ψijΣ), the Kronecker product of Ψ and Σ. Th...
متن کاملCovariance Estimation via Sparse Kronecker Structures
The problem of estimating covariance matrices is central to statistical analysis and is extensively addressed when data are vectors. This paper studies a novel Kronecker-structured approach for estimating such matrices when data are matrices and arrays. Focusing on matrix-variate data, we present simple approaches to estimate the row and the column correlation matrices, formulated separately vi...
متن کاملFlexible Covariance Estimation in Graphical Gaussian Models
In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the WPG family defined by Letac and Massam [Ann. Statist. 35 (2007) 1278–1323] we derive closed-form expressions for Bayes estimators under the entropy and squared-error losses. The WPG family includes the classical inverse of t...
متن کاملLocally Weighted Full Covariance Gaussian Density Estimation
We describe an interesting application of the principle of local learning to density estimation. Locally weighted fitting of a Gaussian with a regularized full covariance matrix yields a density estimator which displays improved behavior in the case where much of the probability mass is concentrated along a low dimensional manifold. While the proposed estimator is not guaranteed to integrate to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 2016
ISSN: 0047-259X
DOI: 10.1016/j.jmva.2016.04.001