Introduction and Overview

  • Qi He
  • Le Yi Wang
  • G. George Yin
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


Traditional system identification taking noise measurement into consideration concentrates on convergence in suitable senses (such as in mean square, in distribution, or with probability one) and rates of convergence. Such asymptotic analysis is inadequate in applications that require precise probability error bounds beyond what are provided by the law of large numbers or the central limit theorem. Especially, for system diagnosis and prognosis and their related complexity analysis, it is essential to understand probabilities of identification errors over a finite data window. For example, in real-time diagnosis, parameter values must be evaluated to determine whether they belong to a “normal” region or a “fault” has occurred. This set-based identification amounts to hypothesis testing, which relies on an accurate probabilistic characterization of parameter estimates.


Stochastic Approximation Identification Error Large Deviation Result Adaptive Noise Cancellation Data Flow Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Qi He, Le Yi Wang, and G. George Yin 2013

Authors and Affiliations

  • Qi He
    • 1
  • Le Yi Wang
    • 2
  • G. George Yin
    • 3
  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA
  2. 2.Department of Electrical and Computer EngWayne State UniversityDetroitUSA
  3. 3.Department of MathematicsWayne State UniversityDetroitUSA

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