The determination of H by using the TF relation :

This paper completes the statistical modeling of the Hubble ow when a Tully-Fisher type relation is used for estimating the absolute magnitude M a p + b from a line width distance indicator p. Our investigation is performed with the aim of providing us with a full understanding of statistical biases due to selection eeects in observation, regardless of peculiar velocities of galaxies. We show that unbiased H-statistics can be obtained by means of the maximum likelihood method as long as the statistical model can be deened. We focus on the statistical models related to the Direct, resp. Inverse, Tully-Fisher relation, when selection eeects on distance, resp. on p, are present. It turns out that the use of the Inverse relation should be preferred, according to robustness criteria. The formal results are ensured by simulations with samples which are randomly generated according to usual characteristics.