This article is cited in 2 papers

On asymptotics of the distributions of some two-step statistical estimators of a mutlidimensional parameter

Yu. Yu. Linke^ab, A. I. Sakhanenko<sup>ba

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: We study the accuracy of estimation of unknown parameters in the case of two-step statistical estimates admitting special representations. An approach to the study of such problems previously proposed by the authors is extended to the case of the estimation of a multidimensional parameter. As a result, we obtain necessary and sufficient conditions for the weak convergence of the normalized estimation error to a multidimensional normal distribution.

Key words: asymptotically normal estimator, improvement of statistical estimates, two-step estimator, multidimensional parameter, regression.

UDC: 519.233.22

Received: 25.04.2012

 English version: Siberian Advances in Mathematics, 2014, 24:2, 119–139

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