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

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

τ n f

... f

, 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−1 f1(vx1)... f1(vxn) dv

∞

0 vn−1 f0(vx1)... f0(vxn) dv

> C.

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