Page 320 - Contributed Paper Session (CPS) - Volume 7

CPS2110 Johann Sebastian B. C. et al.

Constant Linear Quadratic Polynomial
Bootstrap Bootstrap Bootstrap Bootstrap
10% 43% 0% 41% 12% 35% 29% 39% 26%
5% 41% 0% 39% 9% 33% 16% 38% 18%
1% 36% 0% 36% 0% 31% 9% 35% 8%
Table 2. Power of the test under a weak form of overdispersion

Here, the parametric test tends to reject 0 less than half of the time –
possibly because of the weak form of the true variance which does not deviate
significantly from the variance function of a Poisson distribution. However, the
proportion of rejections revealed by using the bootstrap distribution shows
that the score test yields a very low power, which increases with the complexity
of the assumed model of the variance; but still yields to low statistical power.
The next table presents the power of the test under the strong form:
Constant Linear Quadratic Polynomial
t Bootstrap t Bootstrap t Bootstrap t Bootstrap
10% 100% 2% 100% 8% 100% 23% 100% 16%
5% 100% 1% 100% 4% 100% 17% 100% 9%
1% 100% 0% 100% 0% 100% 3% 100% 1%
Table 3. Power of the test under a strong form of overdispersion

When the true form of overdispersion is strong, the parametric test tends
to almost always reject the false 0. However, its bootstrap counterpart
reveals that its actual power is very low, which, again, increases with the
complexity of the assumed model of the variance, yielding to low statistical
power as well. Finally, the last table presents the power of the test under the
transcendental form:
Constant Linear Quadratic Polynomial
t Bootstrap t Bootstrap t Bootstrap t Bootstrap
10% 60% 1% 56% 14% 46% 31% 54% 25%
5% 58% 0% 54% 10% 45% 18% 52% 18%
1% 54% 0% 51% 0% 43% 11% 49% 8%
Table 4. Power of the test under a transcendental from a overdispersion

In this case, the parametric test tends to reject the false 0 only around
half of the time, while its bootstrap counterpart remains to suffer from a very
low power, which improves with the complexity of the assumed model of the
variance. It should be noted, however, that despite the increasing power of the
tests along with the complexity of the assumed form of the variance, it may

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