0 2 4 6 0 0.2 0.4 0.6 0.8 1 h$_{1}$/c$^{1/2}$=0.3006 $_{2}$=(−log(1−h 2 $^{2}$/c))1/2 0 2 4 6 0 0.2 0.4 0.6 0.8 1 h$_{1}$/c$^{1/2}$=0.6683 $_{2}$=(−log(1−h 2 $^{2}$/c))1/2 0 2 4 6 0 0.2 0.4 0.6 0.8 1 h$_{1}$/c$^{1/2}$=0.9520 $_{2}$=(−log(1−h 2 $^{2}$/c))1/2 0 2 4 6 0 0.2 0.4 0.6 0.8 1 h$_{1}$/c$^{1/2}$=0.9995 $_{2}$=(−log(1−h 2 $^{2}$/c))1/2 Figure 3: Profiles of the asymptotic power of the µ -based LR test (solid lines) relative to the asymptotic power envelope (dotted lines) for different values of h$_{1}$$_{/}$√$_{c}$ under the alternative; α = 0 . 05 . µ -based LR test. The value h$_{2}$/h$_{1}$ = 0 corresponds to single-spiked alternatives h$_{1}$ > 0 , h$_{2}$ = 0 , the value h$_{2}$/h$_{1}$ = 1 corresponds to equi-spiked alternatives h$_{1}$ = h$_{2}$ > 0 . The intermediate values of h$_{2}$/h$_{1}$ link the two extreme cases. We do not consider values h$_{2}$/h$_{1}$ > 1, as the power function is symmetric about the 45-degree line in the ( h$_{1}$, h$_{2}$ ) space. Somewhat surprisingly, the power of the LR test along the set of alterna- tives ( h$_{1}$, h$_{2}$ ) corresponding to the same values of the asymptotic power envelope is not a monotone function of h$_{2}$/h$_{1}$. Equi-spiked alternatives typically seem to be particularly difficult to detect by the LR tests. However, for the set of alternatives corresponding to an asymptotic power envelope value of 90%, the single-spiked alternatives are even harder to detect. A natural question is: how does the asymptotic power of the λ - and µ -based LR tests depend on the choice of r , that is, how do those tests perform when 16