This paper proposes a new adaptive algorithm for the implementation of the linearly constrained minimum variance (LCMV) beamformer. The proposed algorithm utilizes the setmembership filtering (SMF) framework and the reduced-rank joint iterative optimization (JIO) scheme. We develop a stochastic gradient (SG) based algorithm for the beamformer design. An effective time-varying bound is employed ...

The present work proposes tests for reduced rank in multivariate regression coefficient matrices, under rather general conditions. A heuristic approach is to first estimate the regressions via standard methods, then compare the coefficient matrix rows (or columns) to assess their redundancy. A formal version of this approach utilizes the distance between an unrestricted coefficient matrix estim...

Space-time adaptive processing (STAP) is an effective strategy for clutter suppression in airborne radar systems. Limited training data, high computational load and the heterogeneity of training data constitute the main challenges in STAP. Most reduced-rank detection approaches, such as eigenvector decomposition, utilise a linear transformation to reduce the problem dimensionality. In this lett...

Minimal Polynomial Extrapolation (MPE) and Reduced Rank Extrapolation (RRE) are two polynomial methods used for accelerating the convergence of sequences of vectors {xm}. They are applied successfully in conjunction with fixedpoint iterative schemes in the solution of large and sparse systems of linear and nonlinear equations in different disciplines of science and engineering. Both methods pro...

This paper introduces a new representation for seasonally cointegrated variables, namely the complex error correction model, which allows statistical inference to be performed by reduced rank regression. The suggested estimators and tests statistics are asymptotically equivalent to their maximum likelihood counterparts. Tables are provided for both asymptotic and finite sample critical values, ...

We propose a new procedure to perform Reduced Rank Regression (RRR) in nonGaussian contexts, based on Multivariate Dispersion Models. Reduced-Rank Multivariate Dispersion Models (RR-MDM) generalise RRR to a very large class of distributions, which include continuous distributions like the normal, Gamma, Inverse Gaussian, and discrete distributions like the Poisson and the binomial. A multivaria...

This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact subset of R. On this approximate eigenbasis the eigenvalues of the covariance function can be expressed as simple functions of the spectral density of the Gau...