Statistical Papers

, Volume 45, Issue 1, pp 15–31 | Cite as

Measuring robustness for weighted distributions: Bayesian perspective

  • Younshik Chung
  • Chansoo Kim


There are many situations where the usual random sample from a population of interest is not available, due to the data having unequal probabilities of entering the sample. The method of weighted distributions models this ascertainment bias by adjusting the probabilities of actual occurrence of events to arrive at a specification of the probabilities of the events as observed and recorded. We consider two different classes of contaminated or mixture of weight functions, Γ a ={w(x):w(x)=(1−ε)w 0(x)+εq(x),qQ} and Γ g ={w(x):w(x)=w 0 1−ε (x)q ε(x),qQ} wherew 0(x) is the elicited weighted function,Q is a class of positive functions and 0≤ε≤1 is a small number. Also, we study the local variation of ϕ-divergence over classes Γ a and Γ g . We devote on measuring robustness using divergence measures which is based on the Bayesian approach. Two examples will be studied.

Key words

Bayesian Robustness ε-contamination Weighted distribution 


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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • Younshik Chung
    • 1
  • Chansoo Kim
    • 1
  1. 1.Department of StatisticsPusan National UniversityPusanKorea

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