I have a set of data that is absolute magnitude of a star and its redshift. Is there any way to compute the value of the hubble parameter given that magnitude and redshift?
Maybe. To calculate the Hubble constant (H=v/d), you need the know the velocity (v≈c*z￼￼) and distance of a distant object (or rather as many objects as possible). The velocity of these objects must be dominated by the expansion of the Universe. So stars in our local group that are still bound to us via gravity wont work. So as long as the stars you use are not really bright or even supernovae in distant galaxies there is no way to get the Hubble constant. If your stars are far enough away, however, you still have get their distance. This you can do with the distance modulus, i.e., difference between absolute and apparent magnitude:
m-M = 5 log(d)-5
So assuming the stars are distant stars for which you also know their apparent magnitude (e.g. Cepheid variables), than yes you can calculate H. If they are just random stars, than not.