On the fisher information of discretized data
Klaus Pötzelberger, Klaus Felsenstein · Journal of Statistical Computation and Simulation · 1993
In this paper we study the loss of Fisher information in approximating a continuous distribution by a multinomial distribution coming from a partition of the sample space into a finite number of intervals. We describe and characterize the Fisher information as a function of the partition chosen especially for location parameters. For a small number of intervals theconsequences of the choice is demonstrated by instructive examples. For increasing numbers of intervals we give the asymptotically optimal partition.