Abstract
We consider minimum φ-divergence estimators of parameters θ of arbitrary dominated models μθ ≪ λ on the real line, based on finite quantizations of i.i.d. observations X
1,…, X
n
from these models. The quantizations are represented by finite interval partitions 𝒫
n
= (A
n1,…, A
nm
n
) of the real line, where m
n
is allowed to increase to infinity for n → ∞. The models with densities f
θ = dμθ/dλ are assumed to be regular in the sense that they admit finite Fisher informations 𝒥θ. In the first place we have in mind continuous models dominated by the Lebesgue measure λ. Owing to the quantizations,
are discrete-model estimators for which the desirable properties (computation complexity, robustness, etc.) can be controlled by a suitable choice of functions φ. We formulate conditions under which these estimators are consistent and efficient in the original models μθ in the sense that
as n → ∞.
Acknowledgments
This work has been supported by the Spanish grants BMF2003-00892, BMF2003-04820, and GV04B-670 and by the Czech grants ASCR A1075403 and MSMTV 1M 0572.