  One important issue commonly encountered in the analysis of microarray data
is to decide which and how many genes should be selected for further studies.
For discriminant microarray data analyses based on statistical models, such as
the logistic regression models, gene selection can be accomplished by a
comparison of the maximum likelihood of the model given the real data,
$\hat{L}(D|M)$, and the expected maximum likelihood of the model given an
ensemble of surrogate data with randomly permuted label, $\hat{L}(D_0|M)$.
Typically, the computational burden for obtaining $\hat{L}(D_0|M)$ is immense,
often exceeding the limits of computing available resources by orders of
magnitude. Here, we propose an approach that circumvents such heavy
computations by mapping the simulation problem to an extreme-value problem. We
present the derivation of an asymptotic distribution of the extreme-value as
well as its mean, median, and variance. Using this distribution, we propose two
gene selection criteria, and we apply them to two microarray datasets and three
classification tasks for illustration.
