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dc.contributor.advisorAlan Edelman.en_US
dc.contributor.authorNadakuditi, Rajesh Raoen_US
dc.contributor.otherWoods Hole Oceanographic Institution.en_US
dc.date.accessioned2007-08-29T19:07:22Z
dc.date.available2007-08-29T19:07:22Z
dc.date.copyright2007en_US
dc.date.issued2006en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/38538
dc.descriptionThesis (Ph. D.)--Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science; and the Woods Hole Oceanographic Institution), 2006.en_US
dc.descriptionThis electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.en_US
dc.descriptionAlso issued in pages. Barker Engineering Library copy: issued in pages.en_US
dc.descriptionIncludes bibliographical references (leaves 193-[201]).en_US
dc.description.abstractThe first part of the dissertation investigates the application of the theory of large random matrices to high-dimensional inference problems when the samples are drawn from a multivariate normal distribution. A longstanding problem in sensor array processing is addressed by designing an estimator for the number of signals in white noise that dramatically outperforms that proposed by Wax and Kailath. This methodology is extended to develop new parametric techniques for testing and estimation. Unlike techniques found in the literature, these exhibit robustness to high-dimensionality, sample size constraints and eigenvector misspecification. By interpreting the eigenvalues of the sample covariance matrix as an interacting particle system, the existence of a phase transition phenomenon in the largest ("signal") eigenvalue is derived using heuristic arguments. This exposes a fundamental limit on the identifiability of low-level signals due to sample size constraints when using the sample eigenvalues alone. The analysis is extended to address a problem in sensor array processing, posed by Baggeroer and Cox, on the distribution of the outputs of the Capon-MVDR beamformer when the sample covariance matrix is diagonally loaded.en_US
dc.description.abstract(cont.) The second part of the dissertation investigates the limiting distribution of the eigenvalues and eigenvectors of a broader class of random matrices. A powerful method is proposed that expands the reach of the theory beyond the special cases of matrices with Gaussian entries; this simultaneously establishes a framework for computational (non-commutative) "free probability" theory. The class of "algebraic" random matrices is defined and the generators of this class are specified. Algebraicity of a random matrix sequence is shown to act as a certificate of the computability of the limiting eigenvalue distribution and, for a subclass, the limiting conditional "eigenvector distribution." The limiting moments of algebraic random matrix sequences, when they exist, are shown to satisfy a finite depth linear recursion so that they may often be efficiently enumerated in closed form. The method is applied to predict the deterioration in the quality of the sample eigenvectors of large algebraic empirical covariance matrices due to sample size constraints.en_US
dc.description.statementofresponsibilityby Rajesh Rao Nadakuditi.en_US
dc.format.extent200, [3] leavesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582
dc.subjectElectrical Engineering and Computer Science.en_US
dc.subject/Woods Hole Oceanographic Institution. Joint Program in Applied Ocean Science and Engineering.en_US
dc.subjectWoods Hole Oceanographic Institution.en_US
dc.subject.lcshStochastic analysisen_US
dc.subject.lcshMathematical modelsen_US
dc.titleApplied stochastic Eigen-analysisen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.en_US
dc.contributor.departmentJoint Program in Applied Ocean Science and Engineering.en_US
dc.contributor.departmentWoods Hole Oceanographic Institution.en_US
dc.identifier.oclc164904935en_US


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