RT Journal Article
T1 Minimum divergence estimators based on grouped data
A1 Menéndez Calleja, María Luisa
A1 Morales González, Domingo
A1 Pardo Llorente, Leandro
A1 Vadja, Igor
AB The paper considers statistical models with real-valued observations i.i.d. by F(x, theta (0)) from a family of distribution functions (F(x, theta); theta is an element of Theta), Theta subset of R-s, s greater than or equal to 1. For random quantizations defined by sample quantiles (F-n(-1)(lambda (1)),..., F-n(-1)(lambda (m-1))) of arbitrary fixed orders 0 < <lambda>(1) < ... < lambda (m-1) < 1, there are studied estimators <theta>(phi ,n) of theta (0) which minimize phi -divergences of the theoretical and empirical probabilities. Under an appropriate regularity, all these estimators are shown to be as efficient (first order, in the sense of Rao) as the MLE in the model quantified nonrandomly by (F-1(lambda (1), theta (0)),..., F-1(lambda (m-1), theta (0))). Moreover, the Fisher information matrix I-m(theta (0), lambda) of the latter model with the equidistant orders lambda = (lambda (j) = j/m : 1 less than or equal to j less than or equal to m-1) arbitrarily closely approximates the Fisher information F(theta (0)) of the original model when m is appropriately large. Thus the random binning by a large number of quantiles of equidistant orders leads to appropriate estimates of the above considered type.
PB Springer
SN 0020-3157
YR 2001
FD 2001-06
LK https://hdl.handle.net/20.500.14352/57864
UL https://hdl.handle.net/20.500.14352/57864
LA eng
NO Sabbatical Program of Complutense University of Madrid
NO CACR
NO DGI
NO CV
DS Docta Complutense
RD 24 abr 2025