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The Stiefel manifold comprises sets of orthonormal vectors in Euclidean space, and as such arises in a variety of contemporary statistical signal processing contexts. Here we consider the problem of estimating the state of a hidden Markov process evolving on this manifold, given noisy observations in the embedding Euclidean space. We describe an approach using sequential Monte Carlo methods, and provide...
Data acquisition in conventional fluorescent-based microarrays takes place after the completion of a hybridization phase. During the hybridization phase, target analytes bind to their corresponding capturing probes on the array. The conventional microarrays attempt to detect presence and quantify amounts of the targets by collecting a single data point, supposedly taken after the hybridization process...
We develop a nonlinear minimax estimator for the classical linear regression model assuming that the true parameter vector lies in an intersection of ellipsoids. We seek an estimate that minimizes the worst-case estimation error over the given parameter set. Since this problem is intractable, we approximate it using semidefinite relaxation, and refer to the resulting estimate as the relaxed Chebyshev...
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