Statistics Graduate Level Quiz
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INTERVAL ESTIMATION
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For a fixed parameter value θ>0\theta>0, suppose n(θ^−θ)→dN(0,V)\sqrt{n}(\widehat{\theta}-\theta)\xrightarrow{d}N(0,V) and a consistent estimator of VV is available. One analyst forms a direct Wald interval for θ\theta. Another applies the delta method to log⁡(θ)\log(\theta), forms a Wald interval on the log scale, and exponentiates its endpoints.
Under the stated fixed-parameter asymptotics, which comparison of the two intervals is most accurate?
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