Ch 9 Interval Estimation
Ch 9. Interval Estimation
Ch 9. Interval Estimation
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<strong>Ch</strong> 9. <strong>Interval</strong> <strong>Estimation</strong><br />
Optimal theory for CI<br />
<strong>Ch</strong>apter 9<br />
Intro<br />
Finding <strong>Interval</strong><br />
Estimator<br />
Optimal theory<br />
for CI<br />
Definition (Probability of false coverage)<br />
For θ ′ ≠ θ, P θ [L(X) ≤ θ ′ ≤ U(X)]<br />
For θ ′ < θ, P θ [L(X) ≤ θ ′ ]<br />
For θ ′ > θ, P θ [θ ′ ≤ U(X)]<br />
Definition<br />
A 1 − α confidence interval with minimum probability of false<br />
coverage is called a Uniformly Most Accurate (UMA) 1 − α<br />
confidence interval.
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