The notion of sampling for second-order q-variate processes is defined. It is shown that if the components of a q-variate process (not necessarily stationary) admits a sampling theorem with some sample spacing, then the process itself admits a sampling theorem with the same sample spacing. A...

It is shown that the finite linear least-squares predictor of a multivariate stationary process converges to its Kolmogorov-Wiener predictor at an exponential rate, provided that the entries of its spectral density matrix are smooth functions. Also, the same rate of convergence holds for the...

A method for simultaneous modelling of the Cholesky decomposition of several covariance matrices is presented. We highlight the conceptual and computational advantages of the unconstrained parameterization of the Cholesky decomposition and compare the results with those obtained using the...

We propose a nonparametric method for identifying parsimony and for producing a statistically efficient estimator of a large covariance matrix. We reparameterise a covariance matrix through the modified Cholesky decomposition of its inverse or the one-step-ahead predictive representation of the...

Chen & Dunson ([3]) have proposed a modified Cholesky decomposition of the form σ = D L L′D for a covariance matrix where D is a diagonal matrix with entries proportional to the square roots of the diagonal entries of Σ and L is a unit lower-triangular matrix solely determining its...

Important results in prediction theory dealing with missing values have been obtained traditionally using difficult techniques based on duality in Hilbert spaces of analytic functions [Nakazi, T., 1984. Two problems in prediction theory. Studia Math. 78, 7-14; Miamee, A.G., Pourahmadi, M., 1988....