On Convergence of Fisher Informations in Continuous Models with Quantized Observations
- Autores: Isabel Molina Peralta, Igor Vajda, Tomas Hobza
- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 14, Nº. 1, 2005, págs. 151-179
- Idioma: inglés
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Resumen
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.
