Testing the Information Matrix Equality with Robust Estimators



Figure 4: Power curves: Student’s t


Let S be the score test statistic, defined in the usual way. Under the
null hypothesis (
p = ), S has a limiting χ2 distribution. Under Hn, as we
show in Appendix C.1,

S →d χ12(δ),

with non-centrality parameter

In conclusion, the score test and the IM tests have the same non-centrality
parameter in their limiting distribution. The power curves (as a function
of
e) of 5%-level tests are given in Figure 4. The differences in power are
entirely due to differences in degrees of freedom: 1 for the score test, 2 for
the IM test with the ML estimator, and 3 for the IM test using any other
M-estimator. The difference in power between the IM tests is small.

4.3 Skewed normal alternative

Let Z — N(0, 1) and denote the distribution of ZI(Z ≤ 0) + (1 + γ) ZI(Z >
0) as FYk (Fernandez and Steel, 1998). Under the sequence of local alterna-
tives

Hn : Y


- Fn = Feskn,


15




More intriguing information

1. Industrial Employment Growth in Spanish Regions - the Role Played by Size, Innovation, and Spatial Aspects
2. Migrating Football Players, Transfer Fees and Migration Controls
3. AJAE Appendix: Willingness to Pay Versus Expected Consumption Value in Vickrey Auctions for New Experience Goods
4. The name is absent
5. Accurate and robust image superresolution by neural processing of local image representations
6. Family, social security and social insurance: General remarks and the present discussion in Germany as a case study
7. The name is absent
8. The name is absent
9. The name is absent
10. Imputing Dairy Producers' Quota Discount Rate Using the Individual Export Milk Program in Quebec