TY - JOUR

T1 - Asymptotic properties of one-step weighted m-estimators with applications to regression

AU - Linke, Yu Yu

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We study the asymptotic behavior of one-step weighted M-estimators based on independent not necessarily identically distributed observations, which approximate consistent weighted M-estimators. We find sufficient conditions for asymptotic normality of these estimators. As an application, we consider some known regression models where the one-step estimation under consideration allows us to construct explicit asymptotically optimal estimators having the same accuracy as the least-squares or quasi-likelihood estimators.

AB - We study the asymptotic behavior of one-step weighted M-estimators based on independent not necessarily identically distributed observations, which approximate consistent weighted M-estimators. We find sufficient conditions for asymptotic normality of these estimators. As an application, we consider some known regression models where the one-step estimation under consideration allows us to construct explicit asymptotically optimal estimators having the same accuracy as the least-squares or quasi-likelihood estimators.

KW - Asymptotic normality

KW - Initial estimator

KW - M-estimators

KW - Newton’s iteration method

KW - Nonlinear regression

KW - One-step M-estimators

KW - One-step weighted M-estimators

UR - http://www.scopus.com/inward/record.url?scp=85052738614&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97T988691

DO - 10.1137/S0040585X97T988691

M3 - Article

AN - SCOPUS:85052738614

VL - 62

SP - 373

EP - 398

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 3

ER -