H0from cosmic chronometers and Type Ia supernovae, with Gaussian Processes and the novel Weighted Polynomial Regression method

In this paper we present new constraints on the Hubble parameter H₀ using: (i) the available data on H (z) obtained from cosmic chronometers (CCH) ; (ii) the Hubble rate data points extracted from the supernovae of Type Ia (SnIa) of the Pantheon compilation and the Hubble Space Telescope (HST) CANDELS and CLASH Multy-Cycle Treasury (MCT) programs; and (iii) the local HST measurement of H₀ provided by Riess et al. (2018), H₀^{ HST}= (73. 451. 66) km/s/Mpc. Various determinations of H₀ using the Gaussian processes (GPs) method and the most updated list of CCH data have been recently provided by Yu, Ratra and Wang (2018). Using the Gaussian kernel they find H₀= (67. 42 4. 75) km/s/Mpc. Here we extend their analysis to also include the most released and complete set of SnIa data, which allows us to reduce the uncertainty by a factor 3 with respect to the result found by only considering the CCH information. We obtain H₀= (67. 06 1. 68) km/s/Mpc, which favors again the lower range of values for H₀ and is in tension with H₀^{ HST}. The tension reaches the 2. 71 level. We round off the GPs determination too by taking also into account the error propagation of the kernel hyperparameters when the CCH with and without H₀^{ HST} are used in the analysis. In addition, we present a novel method to reconstruct functions from data, which consists in a weighted sum of polynomial regressions (WPR). We apply it from a cosmographic perspective to reconstruct H (z) and estimate H₀ from CCH and SnIa measurements. The result obtained with this method, H₀= (68. 90 1. 96) km/s/Mpc, is fully compatible with the GPs ones. Finally, a more conservative GPs+WPR value is also provided, H₀= (68. 45 2. 00) km/s/Mpc, which is still almost 2 away from H₀^{ HST}.