Let X1,...,Xn be a sample from a distribution with density 1 n f x1

Question:

Let X1,...,Xn be a sample from a distribution with density 1

τ n f

...f xn

, where f(x) is either zero for x < 0 or symmetric about zero. The most powerful scale-invariant test for testing H : f = f0 against K : f = f1 rejects when

∞

0 vn−1f1(vx1) ...f1(vxn) dv

∞

0 vn−1f0(vx1) ...f0(vxn) dv > C.

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