Unformatted text preview: is said to be locally asympotically normal (LAN) if the log likelihood ratio can be written as h T Z n1 2 h T Λ h + o P n, (1) where Z n d→ N (0 , Λ) under P n, . Suppose that { P n,h : h ∈ H } is LAN. Show that { P n,h 1 } and { P n,h 2 } are mutually contiguous for any h 1 and h 2 . 4. Suppose that { P n,h : h ∈ H } is LAN. Show that under P n,h we have Z n d→ N (Λ h, Λ). 5. Consider the Hodge supere±cient estimator in the setting in which data X 1 , . . . , X n are sampled i.i.d. from the distribution N ( θ, 1). ²ind a sequence of parameters { θ n } such that the quadratic risk calculated along the sequence grows to inFnity....
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 Fall '05
 MICHAELJORDAN
 Probability, Null hypothesis, Likelihoodratio test, Nij, likelihood ratio, Stat 210B Homework, log likelihood ratio

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