Figure 5: Power curves: Skewed normal
we have, as shown in Appendix B.2,
T →d χq2 (δ)
with non-centrality parameter
δ=
ɪ e e
4π
which is the same for all M-estimators of scale.
Regarding the score test, we show in Appendix C.2 that, under Hn,
S →d χ21 (δ),
with non-centrality parameter
δ=
e2.
The power curves of 5%-level tests are given in Figure 5. The score test
is now considerably more p owerful than the IM test, primarily due to the
larger non-centrality parameter. The difference between the different IM
tests is, again, rather small.
16
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