Question: 20. Let XI' Xm and YI , . . . , Y,. be positive, independent random variables distributed with densities f(x/o) and g(y/'r) respectively. If

20. Let XI"'" Xm and YI , . . . , Y,. be positive, independent random variables distributed with densities f(x/o) and g(y/'r) respectively. If f and g have monotone likelihood ratios in (x, 0) and ( y,1') respectively, there exists a UMP conditional test of H : 1'/0 sAo against 1'/0> Ao given the ancillary statistics U; = X;/Xm and lj = lj/Yn (i = 1, . . . , m - 1; j = 1, .. . , n - 1).

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