Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 28L / d

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- Solution d

Solution

By the Delta method and consistency of the jackknife variance, Slutsky's theorem gives

\frac{T _{n} - θ}{v _{JACK}} \Rightarrow N (0, 1) .

Therefore an asymptotically valid interval is

[T_{n} - z_{1 - α /2} v_{JACK}, T_{n} + z_{1 - α /2} v_{JACK}] .

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