Testing the Information Matrix Equality with Robust Estimators

Figure 5: Power curves: Skewed normal

we have, as shown in Appendix B.2,

T →^d χq² (δ)

with non-centrality parameter

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=

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.

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