Resumen de On Convergence of Fisher Informations in Continuous Models with Quantized Observations
Isabel Molina Peralta, Igor Vajda, Tomas Hobza
Continuous location models with real observations and well defined Fisher information are considered and reduction of the Fisher information due to quantizations of the observation space into m intervals is studied. In fact, generalized Fisher informations of orders a = 1 are considered where a = 2 corresponds to the classical Fisher information. By an example it is argued that in some models the information of order a = 2 is infinite while the informations of some orders a ? 2 are finite. Among the studied problems is the existence of optimal quantizations which maximize the reduced information for fixed m and a = 1 and the construction of simple and practically applicable quantizations for which the reduction converges to zero when m ? 8, uniformly for all a = 1. The rate of this convergence is estimated for all a = 1 and directly evaluated for a = 1 and a = 2. For special models the reductions are directly evaluated for m = 1, 2, ... either analytically or numerically.
