  We propose a new approach to improve the precision of astrophysical parameter
constraints for the 21cm signal from the epoch of reionisation (EoR). Our
method introduces new sets of summary statistics, hereafter `evolution
compressed' statistics, which quantify the spectral evolution of the 2D spatial
statistics computed at fixed redshift. We defined such compressed statistics
for power spectrum (PS), wavelet scattering transforms (WST), and wavelet
moments (WM), which also characterise non-Gaussian features. To compare these
different statistics, along with the 3D power spectrum, we estimated their
Fisher information on three cosmological parameters from an ensemble of
simulations of 21cm EoR data, both in noiseless and noisy scenarios using
Square Kilometre Array (SKA) noise levels equivalent to 100 and 1000 hours of
observations. We also compare wavelet statistics, in particular WST, built from
standard directional Morlet wavelets, as well as from a set of isotropic
wavelets derived from the binning window function of the 2D power spectrum. For
the noiseless case, the compressed wavelet statistics give constraints that are
up to five times more precise than those obtained from the 3D isotropic power
spectrum. At the same time, for 100h SKA noise, from which it is difficult to
extract non-Gaussian features, compressed wavelet statistics still give over
30\% tighter constraints. We find that the wavelet statistics with wavelets
derived from the power-spectrum binning window function provide the tightest
constraints of all the statistics, with the WSTs seemingly performing better
than the WMs, in particular when working with noisy data. The findings of this
study demonstrate that evolution-compressed statistics extract more information
than usual 3D isotropic power-spectra approaches and that our wavelet-based
statistics can consistently outmatch power-spectrum-based statistics.
