Testing the Information Matrix Equality with Robust Estimators

(a)

0      0.5      1      1.5      2      2.5

x 10 3

Figure 3: Power curves: (a) asymmetric contamination at x =10
and (b) symmetric contamination at x = -10, 10

bution. The ordering is unambiguous: the IM test with the TB estimator is
far more powerful than with the MAD or ML estimator. Using the MAD is
slightly more powerful than using ML. The TB estimator with 25% break-
down point is a compromise between the ML estimator which is efficient but
has 0% breakdown point, and the MAD estimator, which has 50% break-
down point but is very inefficient. This compromise yields a more powerful
IM test.

4.2 Student’s t alternative

Consider the sequence of local alternatives

Hn : Y - Fn = Ft(   .)    ( e > 0)

where F_t(_p) is the distribution function of a Student’s t variate with p degrees
of freedom. In Appendix B.1 it is shown that, under H_n,

T →^d χq² (δ)

with non-centrality parameter

δ

for all M-estimators of scale.

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