  We discuss a robust data analysis method to detect a stochastic background of
gravitational waves in the presence of non-Gaussian noise. In contrast to the
standard cross-correlation (SCC) statistic frequently used in the stochastic
background searches, we consider a {\it generalized cross-correlation} (GCC)
statistic, which is nearly optimal even in the presence of non-Gaussian noise.
The detection efficiency of the GCC statistic is investigated analytically,
particularly focusing on the statistical relation between the false-alarm and
the false-dismissal probabilities, and the minimum detectable amplitude of
gravitational-wave signals. We derive simple analytic formulae for these
statistical quantities. The robustness of the GCC statistic is clarified based
on these formulae, and one finds that the detection efficiency of the GCC
statistic roughly corresponds to the one of the SCC statistic neglecting the
contribution of non-Gaussian tails. This remarkable property is checked by
performing the Monte Carlo simulations and successful agreement between
analytic and simulation results was found.
