Applied Stochastic Eigen-Analysis

Abstract

The 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 IKailath. This methodology is extended to develop new parametric techniques for testing and estimation. Unlike ted%- niques 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.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2007
Accession Number
ADA470318

Entities

People

  • Rajesh R. Nadakuditi

Organizations

  • Woods Hole Oceanographic Institution

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies
  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Aircrafts
  • Algorithms
  • Data Science
  • Differential Equations
  • Distribution Functions
  • Electrical Engineering
  • Information Science
  • Matrix Theory
  • Measurement
  • Plastic Explosives
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Signal Processing
  • Statistical Algorithms
  • Statistical Inference
  • Theorems

Readers

  • Linear Algebra
  • Neural Network Machine Learning.
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms