Local sensitivity analysis for selection bias

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Double the confidence region
S. Eguchi, ISM GUAS This talk is a part of
co-work with J. Copas, University of Warwick
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Tubular Neighborhood

M
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Sensitivity method

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Confidence region

For the empirical distribution from
The conventional confidence region is
where satisfies
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Strong model for incomplete observation

Let Y h(Z) be many-to-one mapping.
then Y has
If Z has
Cf. EM algorithm
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Mis-specification

General misspecification model
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Actual incomplete observation

where
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Ideal Model and Our Situation

Ideal model
Our situation
Semi-parametric
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Confidence region (weak model)

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MCAR

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MAR

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Random design
m groups comparison

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Two MLEs
Unobserved MLE

Observed MLE
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Ideals of two MLEs

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Expectation of Scores

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Covariance of Scores

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Biases of two MLEs

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Asymptotic variance

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Joint (S,T )

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Conditional S T

• The conditional distribution

If T were observed, the C. R. would
be
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Acceptability
T has the asymptotic distribution

We assume
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Envelope region

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The worst case

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Confidence region

For the empirical distribution from
The conventional confidence region is
Where satisfies
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Bound of Envelope region

where
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l 0.3
l 0.3
2
1
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l 0.05
l 0.9
2
1
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l 0.1
l 0.1
2
1
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Discussion

Double the confidence interval
The worst case occurs when