Measuring robustness for weighted distributions: Bayesian perspective |
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Authors: | Younshik Chung Chansoo Kim |
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Institution: | (1) Department of Statistics, Pusan National University, 609-735 Pusan, Korea |
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Abstract: | 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),q∈Q} and Γ
g
={w(x):w(x)=w
0
1−ε
(x)q
ε(x),q∈Q} 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. |
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Keywords: | Bayesian Robustness ε -contamination Weighted distribution |
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