This article is cited in 1 paper

Probability theory and mathematical statistics

On asymptotics of the distribution of a two-step statistical estimator of a one-dimensional parameter

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

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

Abstract: The authors' approach to study two-step estimators of one-dimensional unknown parameters is extended to a wider classes of the first- and second-step estimators which include well known M-estimators. Under general restrictions necessary and sufficient conditions are found for the normalized difference between the second-step estimator and the unknown parameter to converge weakly to an arbitrary distribution.

Keywords: two-step estimators, impovement of statistical estimators, limit distribution, asymptotical normality, M-estimators, regression.

UDC: 519.23

MSC: 62F12

Received October 3, 2013, published November 8, 2013