# Robust statistics toward detection of the 21 cm signal from the Epoch of Reionisation

## TL;DR

This paper introduces a robust statistical method using Kernel Density Estimation to improve detection of the 21 cm signal from the Epoch of Reionisation, effectively reducing foreground contamination in observational data.

## Contribution

The paper presents a novel KDE-based approach for separating foregrounds from the 21 cm signal without assuming Gaussianity, applied to real MWA data with demonstrated improvements.

## Key findings

- Reduced foreground contamination by a factor of 2-3 for k < 0.3hMpc^{-1}
- Effective discrimination of foregrounds using histogram moments and independent fields
- Demonstrated method's superiority over traditional power spectrum estimators

## Abstract

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.