  We develop a general method for power spectrum analysis of three dimensional
redshift surveys. We present rigorous analytical estimates for the statistical
uncertainty in the power and we are able to derive a rigorous optimal weighting
scheme under the reasonable (and largely empirically verified) assumption that
the long wavelength Fourier components are Gaussian distributed. We apply the
formalism to the updated 1-in-6 QDOT IRAS redshift survey, and compare our
results to data from other probes: APM angular correlations; the CfA and the
Berkeley 1.2Jy IRAS redshift surveys. Our results bear out and further quantify
the impression from e.g.\ counts-in-cells analysis that there is extra power on
large scales as compared to the standard CDM model with $\Omega h\simeq 0.5$.
We apply likelihood analysis using the CDM spectrum with $\Omega h$ as a free
parameter as a phenomenological family of models; we find the best fitting
parameters in redshift space and transform the results to real space. Finally,
we calculate the distribution of the estimated long wavelength power. This
agrees remarkably well with the exponential distribution expected for Gaussian
fluctuations, even out to powers of ten times the mean. Our results thus reveal
no trace of periodicity or other non-Gaussian behavior.
