Unformatted text preview: θ units to the right 5. Let X 1 ,X 2 ,... ,X n be a random sample from a distribution with pdf f ( x ; θ ). Under the “regularity conditions” for the CRLB, (a) Find the asymptotic distribution of n s i =1 ∂ ∂θ ln f ( X i ; θ ) (b) What does 1 n n s i =1 p∂ 2 ∂θ 2 ln f ( X i ; θ ) P converge in probability to? (Explain.) 6. [Required for 5520 Only] Let X 1 ,X 2 ,... ,X n be a random sample from a distribution with pdf f ( x ; θ ). A statistic M is minimal sufcient for this model if it is su²cient and a function of every other set of su²cient statistics. Suppose that T = t ( v X ) is any statistic. Show that T is minimal su²cient if the following condition holds for any vx and vy . f ( vx ; θ ) f ( vy ; θ ) is independent of θ ⇔ t ( vx ) = t ( vy ) ....
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 Fall '11
 Manuel
 Normal Distribution, Probability theory, µ, X1, Sufficient statistic

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