  We present an experimental study of missing level statistics of
three-dimensional chaotic microwave cavities. The investigation is reinforced
by the power spectrum of level fluctuations analysis which also takes into
account the missing levels. On the basis of our data sets we demonstrate that
the power spectrum of level fluctuations in combination with short- and
long-range spectral fluctuations provides a powerful tool for the determination
of the fraction of randomly missing levels in systems that display wave chaos
such as the three-dimensional chaotic microwave cavities. The experimental
results are in good agreement with the analytical expressions that explicitly
take into account the fraction of observed levels. We also show that in the
case of incomplete spectra with many unresolved states the above procedures may
fail. In such a case the random matrix theory calculations can be useful for
the determination of missing levels.
