We introduce a reduced rank technique for testing for common deterministic shifts. The reduced rank approach is analysed also in the context of super exogenity and an alternative test for super-exogeneity is proposed. One important advantage of this approach is that departing from the unrestricted model we depart from a more general model that does not impose a priori which are the target and t...

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We review both full-rank and reduced-rank parameterizations for correlation matrices. In particular, the full-rank parameterizations of Rebonato (1999d) and Schoenmakers and Coffey (2000), the reduced-rank angle parameterization of Rebonato (1999d) and Rebonato and Jäckel (1999), and the well known zeroed-eigenvalues reduced-rank approximation are described in detail. Numerical examples are pro...

We show that for several notions of rank including tensor rank, Waring rank, and generalized rank with respect to a projective variety, the maximum value of rank is at most twice the generic rank. We show that over the real numbers, the maximum value of the real rank is at most twice the smallest typical rank, which is equal to the (complex) generic rank.

Explaining the maintenance of sexual reproduction remains one of the greatest challenges in biology. The theoretical oddity of sex is based on at least three advantages that asexual organisms have over sexual ones: 1Asexuals, by not producing males, have a two fold advantage over sexuals, regarding the number of reproductive individuals; 2Sexuals have an evolutionary disadvantage over asexuals,...

The goal of this study is to compare the performances of the ensemble Kalman filter and a reduced-rank extended Kalman filter when applied to different dynamic regimes. Data assimilation experiments are performed using an eddy-resolving quasi-geostrophic model of the winddriven ocean circulation. By changing eddy viscosity, this model exhibits two qualitatively distinct behaviors: strongly chao...

In this work we propose schemes for joint modelorder and step-size adaptation of reduced-rank adaptive filters. The proposed schemes employ reduced-rank adaptive filters in parallel operating with different orders and step sizes, which are exploited by convex combination strategies. The reduced-rank adaptive filters used in the proposed schemes are based on a joint and iterative decimation and ...

Chicago, Illinois " Those who seek should not stop seeking until they find. When they find, they will be disturbed. When they are disturbed, they will rule, and when they rule, they will rest. " The Gospel of Thomas 2:1-4 iii ACKNOWLEDGMENTS My deepest gratitude goes to my advisor Prof. Arye Nehorai for his permanent support, his excellent guidance, and patience during my graduate studies. This...

The SAR model is widely used in spatial econometrics to model Gaussian processes on a discrete spatial lattice, but for large datasets, fitting it becomes computationally prohibitive, and hence, its usefulness can be limited. A computationally-efficient spatial model is the spatial random effects (SRE) model, and in this article, we calibrate it to the SAR model of interest using a generalisati...

This paper proposes a novel linear estimator named stochastic MV-PURE estimator, developed for the stochastic linear model, and designed to provide improved performance over the linear minimum mean square error (MMSE) Wiener estimator in cases prevailing in practical, real-world settings, where at least some of the second-order statistics of the random vectors under consideration are only imper...