Suppose X1, , Xn are i i d N(0, 2) Let Tn,1 Y n n1 n i 1 Yi , where Yi X2 i Also, let Tn,2 (2n)1 n i 1(Yi Y n)2 For testing 1 versus 1, does the Pitman asymptotic relative efficiency of Tn,1 with respect to Tn,2 exist If so, find it Section 15 3 ...

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Suppose X1,..., Xn are i.i.d. N(0, 2). Let Tn,1 = Y n = n1 n i=1 Yi

Question:

Suppose X1,..., Xn are i.i.d. N(0, σ2). Let Tn,1 = Y¯

n =

n−1 n i=1 Yi , where Yi = X2 i . Also, let Tn,2 = (2n)−1 n i=1(Yi − Y¯

n)2. For testing

σ = 1 versus σ > 1, does the Pitman asymptotic relative efficiency of Tn,1 with respect to Tn,2 exist? If so, find it.
Section 15.3

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