Stability and weak stability

  • Wlodzimierz Bryc
Part of the Lecture Notes in Statistics book series (LNS, volume 100)


The stability problem is the question of to what extent the conclusion of a theorem is sensitive to small changes in the assumptions. Such description is, of course, vague until the questions of how to quantify the departures both from the conclusion and from the assumption are answered. The latter is to some extent arbitrary; in the characterization context, typically, stability reasoning depends on the ability to prove that small changes (measured with respect to some measure of smallness) in assumptions of a given characterization theorem result in small departures (measured with respect to one of the distances of distributions) from the normal distribution.


Characteristic Function Cumulative Distribution Function Normal Case Conditional Variance Bivariate Normal Distribution 
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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Wlodzimierz Bryc
    • 1
  1. 1.Department of MathematicsUniversity of CincinnatiCincinnatiUSA

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