Author： Menéndez M.
Publisher： Springer Publishing Company
ISSN： 0020-3157
Source： Annals of the Institute of Statistical Mathematics, Vol.53, Iss.2, 2001-06, pp. : 277-288
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Abstract
The paper considers statistical models with real-valued observations i.i.d. by F(x, _0) from a family of distribution functions (F(x, ); ∈ Θ), Θ ⊂ R^s, s ≥ 1. For random quantizations defined by sample quantiles (F_n^−1 (_1),…, F_n^−1 (_m−1)) of arbitrary fixed orders 0 < _1="" …="">< _m-1="">< 1,="" there="" are="" studied="" estimators="" _,n="" of="" _0="" which="" minimize="" -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="" (_1,_0),…,="" f^−1="" (_m−1,="" _0)).="" moreover,="" the="" fisher="" information="" matrix="" i_m="" (_0,="" )="" of="" the="" latter="" model="" with="" the="" equidistant="" orders="" ="(_j" =="" j/m="" :="" 1="" ≤="" j="" ≤="" m="" -="" 1)="" arbitrarily="" closely="" approximates="" the="" fisher="" information="" j(_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.="">
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