  The association between two random variables is often of primary interest in
statistical research. In this paper semiparametric models for the association
between random vectors X and Y are considered which leave the marginal
distributions arbitrary. Given that the odds ratio function comprises the whole
information about the association the focus is on bilinear log-odds ratio
models and in particular on the odds ratio parameter vector {\theta}. The
covariance structure of the maximum likelihood estimator {\theta}^ of {\theta}
is of major importance for asymptotic inference. To this end different
representations of the estimated covariance matrix are derived for conditional
and unconditional sampling schemes and different asymptotic approaches
depending on whether X and/or Y has finite or arbitrary support. The main
result is the invariance of the estimated asymptotic covariance matrix of
{\theta}^ with respect to all above approaches. As applications we compute the
asymptotic power for tests of linear hypotheses about {\theta} - with emphasis
to logistic and linear regression models - which allows to determine the
necessary sample size to achieve a wanted power.
