  We study the statistical properties of the time delay matrix $Q$ in the
context of quantum transport through a chaotic cavity, in the absence of
time-reversal invariance. First, we approach the problem from the point of view
of random matrix theory, and obtain exact results that provide the average
value of any polynomial function of $Q$. We then consider the problem from the
point of view of the semiclassical approximation, obtaining the entire
perturbation series for some energy-dependent correlation functions. Using
these correlation functions, we show agreement between the random matrix and
the semiclassical approaches for several statistical properties.
