Let P be uniform on 0, Let n 0 h n Calculate the limit of n H2(P0 , P0 h n) If h 0, let n be the UMP level test which rejects when the maximum order statistic is too large Evaluate the limit of the power of n against the alternative n ...

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Let P be uniform on [0, ]. Let n = 0 + h/n. Calculate the limit of

Question:

Let Pθ be uniform on [0, θ]. Let θn = θ0 + h/n. Calculate the limit of n H2(Pθ0 , Pθ0+h/n). If h > 0, let φn be the UMP level-α test which rejects when the maximum order statistic is too large. Evaluate the limit of the power of φn against the alternative θn.

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