Asymptotic properties of one-step M-estimators

Abstract

We study the asymptotic behavior of one-step M-estimators based on not necessarily independent identically distributed observations. In particular, we find conditions for asymptotic normality of these estimators. Asymptotic normality of one-step M-estimators is proven under a wide spectrum of constraints on the exactness of initial estimators. We discuss the question of minimal restrictions on the exactness of initial estimators. We also discuss the asymptotic behavior of the solution to an M-equation closest to the parameter under consideration. As an application, we consider some examples of one-step approximation of quasi-likelihood estimators in nonlinear regression.

Keywords:

• One-step M-estimator
• asymptotic normality
• initial estimator
• nonlinear regression

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62F12
• 62J02

Notes

1 Note

Somewhat different proof of this lemma is contained in Linke and Sakhanenko (2016).

Additional information

Funding

This work was supported by the Russian Foundation for Basic Research, under grant 18–01–00074; and by the Program for Fundamental Scientific Research of the SB RAS, No I.1.3., under Grant 0314-2016-0008.