36 write n n n a n x n n x n n a n 1 x n n x n o 1 o

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Write n ̂ n n a n X ̄ n n X ̄ n n a n 1 X ̄ n n X ̄ n o 1 O p 1 n X ̄ n o p 1 because n a n 1 o 1 and X ̄ n O p 1 . It follows by the asymptotic equivalence lemma that n ̂ n and n X ̄ n have the same asymptotic distribution, so n ̂ n d Normal 0, 2 even though E ̂ n a n and 2 Var n ̂ n  a n 2 2 . 37
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