On the Fisher Information of Discretized Data

In this paper we study the loss of Fisher information in approximating a continous distribution by a multinominal 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 the consequences of the choice is demonstrated by instructive examples. For increasing number of individuals we give the asymptotically optimal partition. (author's abstract)