Geodesic
On conditions for asymptotic normality of Fisher's one-step estimators in one-parameter families of distributions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 464-475

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We consider asymptotic behavior of one-step statistical estimators introduced by R. Fisher as approximations for consistent maximum likelihood estimators. Some sufficient conditions are found for these one-step estimators to be asymptotically normal even in the cases when either the maximum likelihood estimators may not exist or exist but be inconsistent. Investigated are connections between the smoothness conditions for the density of the sample distribution and the rate of proximity of the preliminary estimator and the parameter which are needed for fulfillment of the properties under considerations.
Keywords: one-step estimators, asymptotical normality, maximum likelihood estimator, Newton's method, preliminary estimator, proximity of estimation. 
@article{SEMR_2014_11_a34,
     author = {Yu. Yu. Linke and A. I. Sakhanenko},
     title = {On conditions for  asymptotic normality  of {Fisher's} one-step estimators in one-parameter families of  distributions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {464--475},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a34/}
}
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Yu. Yu. Linke; A. I. Sakhanenko. On conditions for  asymptotic normality  of Fisher's one-step estimators in one-parameter families of  distributions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 464-475. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a34/