Estimation of low-rank covariance function

Adjoints and low-rank covariance representation

Quantitative measures of the uncertainty of Earth system estimates can be as important as the estimates themselves. Direct calculation of second moments of estimation errors, as described by the covariance matrix, is impractical when the number of degrees of freedom of the system state is large and the sources of uncertainty are not completely known. Theoretical analysis of covariance equations...

Nonparametric estimation of low rank matrix valued function

Let A : [0, 1] → Hm (the space of Hermitian matrices) be a matrix valued function which is low rank with entries in Hölder class Σ(β, L). The goal of this paper is to study statistical estimation of A based on the regression model E(Yj |τj , Xj) = 〈A(τj), Xj〉, where τj are i.i.d. uniformly distributed in [0, 1], Xj are i.i.d. matrix completion sampling matrices, Yj are independent bounded respo...

Parameter expansion for estimation of reduced rank covariance matrices

1 ‘Parameter expanded’ and standard expectation maximisation algorithms are de2 scribed for reduced rank estimation of covariance matrices by restricted maximum 3 likelihood, fitting the leading principal components only. Convergence behaviour of 4 these algorithms is examined for several examples and contrasted to that of the aver5 age information algorithm, and implications for practical anal...

High Dimensional Low Rank and Sparse Covariance Matrix Estimation via Convex Minimization

This paper introduces a general framework of covariance structures that can be verified in many popular statistical models, such as factor and random effect models. The new structure is a summation of low rank and sparse matrices. We propose a LOw Rank and sparsE Covariance estimator (LOREC) to exploit this general structure in the high-dimensional setting. Analysis of this estimator shows that...

Rank Analysis of Covariance