This chapter surveys the importance of reduced rank regression techniques (RRR) for modelling economic and ?nancial time series. We mainly focus on models that are capable to reproduce presence common dynamics among variables such as serial correlation feature multivariate autoregressive index models. Cointegration analysis, which RRR plays a central role, is not discussed in this it deserves s...

the presence of noise in geophysical measurements has undesirable effects on the seismic data. one of the important problems in seismic data processing is attenuation of the noise to the desired form and keeping the original signal. contamination of seismic data with noise prevents obtaining a proper image of geological structures and seismic data interpretation. in some of the receivers the no...

This paper presents a novel adaptive reduced-rank multi-input multi-output (MIMO) equalization scheme and algorithms based on alternating optimization design techniques for MIMO spatial multiplexing systems. The proposed reduced-rank equalization structure consists of a joint iterative optimization of two equalization stages, namely, a transformation matrix that performs dimensionality reductio...

We specify a class of Gaussian rank-r latent models for cross-covariance. We show by construction that any variance-covariance matrix for the observed variables induced by rank-r reduced-rank regression can be induced by a rank-r latent model. 1 Model specification Basic terms are introduced which will be used to state the result. 1.1 Rank-r constraint models Let p be the number of X-variables ...

relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $m$, called {em $tau$-rank of} $m$, which coincides with the reduced rank of $m$ whenever $tau$ is the goldie torsion theory. it is shown that the $tau$-rank of $m$ is measured by the length of certain decompositions of the $tau$-injective hull of $m$. moreover, some relations between the $tau$-rank of $m$ and c...

Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...

where A is an unknown p× n matrix of coefficients and E is an unobserved m× n random noise matrix with independent mean zero and variance σ. We want to find an estimate  such that ||Y −XÂ|| is small. If we use standard least square estimation directly to estimate A in (1.1) without adding any constraints, then it is just the same as regressing each response on the predictors separately. In thi...