Robust statistics toward detection of the 21 cm signal from the Epoch of
  Reionisation
  We explore methods for robust estimation of the 21 cm signal from the Epoch
of Reionisation (EoR). A Kernel Density Estimator (KDE) is introduced for
measuring the spatial temperature fluctuation power spectrum from the EoR. The
KDE estimates the underlying probability distribution function of fluctuations
as a function of spatial scale, and contains different systematic biases and
errors to the typical approach to estimating the fluctuation power spectrum.
Extraction of histograms of visibilities allows moments analysis to be used to
discriminate foregrounds from 21 cm signal and thermal noise. We use the
information available in the histograms, along with the statistical
dis-similarity of foregrounds from two independent observing fields, to
robustly separate foregrounds from cosmological signal, while making no
assumptions about the Gaussianity of the signal. Using two independent
observing fields to robustly discriminate signal from foregrounds is crucial
for the analysis presented in this paper. We apply the techniques to 13 hours
of Murchison Widefield Array (MWA) EoR data over two observing fields. We
compare the output to that obtained with a comparative power spectrum
estimation method, and demonstrate the reduced foreground contamination using
this approach. Using the second moment obtained directly from the KDE
distribution functions yields a factor of 2-3 improvement in power for k <
0.3hMpc^{-1} compared with a matched delay space power estimator, while
weighting data by additional statistics does not offer significant improvement
beyond that available for thermal noise-only weights.
