Generalized linear mixed models(GLMMs) are frequently used for the analysis of longitudinal categorical data when the subject-specific effects is of interest. In GLMMs, the structure of the random effects covariance matrix is important for the estimation of fixed effects and to explain subject and time variations. The estimation of the matrix is not simple because of the high dimension and the ...

Covariances play a fundamental role in the theory of time series and they are critical quantities that are needed in both spectral and time domain analysis. Estimation of covariance matrices is needed in the construction of confidence regions for unknown parameters, hypothesis testing, principal component analysis, prediction, discriminant analysis among others. In this paper we consider both l...

We consider the problem of finding the smallest adjustment to a given symmetric n × n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and inequalities, and in addition is positive semidefinite. This least-squares covariance adjustment problem is a convex optimization problem, and can be efficiently solved using standard methods when the ...

In a fuzzy classifier with ellipsoidal regions, each cluster is approximated by a center and a covariance matrix, and the membership function is calculated using the inverse of the covariance matrix. Thus when the number of training data is small, the covariance matrix becomes singular and the generalization ability is degraded. In this paper, during the symmetric Cholesky factorization of the ...

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351–376...

In classifying high-dimensional patterns such as stellar spectra by a Gaussian classifier, the covariance matrix estimated with a small-number sample set becomes unstable, leading to degraded classification accuracy. In this paper, we investigate the covariance matrix estimation problem for small-number samples with high dimension setting based on minimum description length (MDL) principle. A n...

A random vector xi ∈ R is said to be drawn from a spiked covariance model if it can written in the form xi = F ∗ √ Γξi + wi where F ∗ ∈ Rd×r is a fixed matrix with orthonormal columns; Γ = diagγ1, . . . , γr} is a diagonal matrix with γ1 ≥ γ2 ≥ · · · ≥ γr > 0; ξi ∈ R is a zero-mean random vector with identity covariance, and wi is a zero-mean random vector, independent of ξi, and with identity ...

This paper addresses the problem of estimating the covariance matrix reliably when the assumptions, such as Gaussianity, on the probabilistic nature of multichannel data do not necessarily hold. Multivariate spatial sign and rank functions, which are generalizations of univariate sign and centered rank, are introduced. Furthermore, spatial rank covariance matrix and spatial Kendall’s tau covari...

We present a novel method for estimating tree-structured covariance matrices directly from observed continuous data. Specifically, we estimate a covariance matrix from observations of p continuous random variables encoding a stochastic process over a tree with p leaves. A representation of these classes of matrices as linear combinations of rank-one matrices indicating object partitions is used...

We present an algorithm for clustering multivariate normal distributions based upon the symmetric, Kullback-Leibler divergence. Optimal mean vector and covariance matrix of the centroid normal distribution are derived and a set of Riccati matrix equations is used to find the optimal covariance matrix. The solutions are found iteratively by alternating the intermediate mean and covariance soluti...