Savin, N. E. and A. H. Würtz, Power of Tests in
Binary Response Models. Econometrica, vol. 67, 1999.
Abstract
Most hypotheses tested in binary response models are composite, that is,
the null hypothesis restricts only a subset of the parameters. The remaining
parameters are referred to as nuisance parameters. The null hypothesis
is usually that one or more of the slope coefficients are zero. Typically,
the sequence of alternatives of interest is one in which the slope coefficients
are increasing in absolute value. In this paper, we prove for any fixed
sample size that the power goes to zero for this sequence of alternatives
in cases which often occur in practice.