ABSTRACT Accurate estimation of the Hubble constant, and other cosmological parameters, from distances measured by cosmic gravitational wave sirens requires sufficient allowance for the dark energy evolution. We demonstrate how model-independent statistical methods, specifically Gaussian process regression, can remove bias in the reconstruction of H(z), and can be combined to model independently with supernova distances. This allows stringent tests of both H0 and Λ cold dark matter, and can detect unrecognized systematics. We also quantify the redshift systematic control necessary for the use of dark sirens, showing that it must approach spectroscopic precision to avoid significant bias.