(Solution Library) Given f(x ; θ)=1 / θ, 00, formally compute the reciprocal of n E[(partial ln f(X ; θ))/(partial θ)]^2 Compare this


Question: Given \(f(x ; \theta)=1 / \theta, 00\), formally compute the reciprocal of

\[n \mathrm{E}\left\{\left[\frac{\partial \ln f(X ; \theta)}{\partial \theta}\right]^{2}\right\}\]

Compare this with the variance of \((n+1) Y_{(n)} / n\), where \(Y_{(n)}\) is the largest order statistic of a random sample of size \(n\) from this distribution. Comment.

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