Covariance Reducing Models: An Alternative to Spectral Modeling of Covariance Matrices
نویسنده
چکیده
We introduce covariance reducing models for studying the sample covariance matrices of a random vector observed in different populations. The models are based on reducing the sample covariance matrices to an informational core that is sufficient to characterize the variance heterogeneity among the populations. They possess useful equivariance properties and provide a clear alternative to spectral models for covariance matrices. Some key words: Central subspace, Dimension reduction, Envelopes, Grassmann manifolds, Reducing subspaces.
منابع مشابه
Forming Different-Complexity Covariance-Model Subspaces through Piecewise-Constant Spectra for Hyperspectral Image Classification
A key factor in classifiers based on the normal (or Gaussian) distribution is the modeling of covariance matrices. When the number of available training pixels is limited, as often is the case in hyperspectral image classification, it is necessary to limit the complexity of these covariance models. An alternative to reducing the complexity uniformly over the whole feature space, is to form orth...
متن کاملLarge Sample Covariance Matrices without Independence Structures in Columns
The limiting spectral distribution of large sample covariance matrices is derived under dependence conditions. As applications, we obtain the limiting spectral distributions of Spearman’s rank correlation matrices, sample correlation matrices, sample covariance matrices from finite populations, and sample covariance matrices from causal AR(1) models.
متن کاملCovariance Estimation: The GLM and Regularization Perspectives
Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent high-dimensional data environment where enforcing the positive-definiteness constraint could be computationally expensive. We provide a survey of the progress made in ...
متن کاملOn limiting spectral distribution of large sample covariance matrices by VARMA(p,q)
We studied the limiting spectral distribution of large-dimensional sample covariance matrices of a stationary and invertible VARMA(p,q) model. Relationship of the power spectral density and limiting spectral distribution of large population dimensional covariance matrices of ARMA(p,q) is established. The equation about Stieltjes transform of large-dimensional sample covariance matrices is also ...
متن کاملVariable Selection for Joint Mean and Covariance Models via Penalized Likelihood
In this paper, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models for longitudinal data. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. We further show that the proposed estimation method can correctly identify the true ...
متن کامل