5 papers
Riemannian Geometry with differentiable ambient space and metric operator
Du Nguyen
We show Riemannian geometry could be studied by identifying the tangent bundle of a Riemannian manifold with a subbundle of the trivial bundle $\mathcal{M} \times \ma…
Riemannian gradient and Levi-Civita connection for fixed-rank matrices
Du Nguyen
We provide formulas for Riemannian gradient and Levi-Civita connection for a family of metrics on fixed-rank matrix manifolds, based on nonconstant metrics on Stiefel manifolds.
A theorem of Kalman and minimal state-space realization of Vector Autoregressive Models
Du Nguyen
We introduce a concept of (AR)state-space realization that could be applied to all transfer functions with invertible. We s…
Vector Autoregressive Moving Average Model with Scalar Moving Average
Du Nguyen
We show Vector Autoregressive Moving Average models with scalar Moving Average components could be estimated by generalized least square (GLS) for each fixed moving average polynom…
An Explicit Formula for Likelihood Function for Gaussian Vector Autoregressive Moving-Average Model Conditioned on Initial Observables with Application to Model Calibration
Du Nguyen
We derive an explicit formula for likelihood function for Gaussian VARMA model conditioned on initial observables where the moving-average (MA) coefficients are scalar. For fixed M…