Some aspects of hadamard differentiability on regression L-estimators

Abstract

We propose a modified version of Welsh's (1987) one-step L-estimator of regression to improve the stability of the estimator and simplify the computation of the estimator. This modified L-estimator of regression is equivalent to a Hadamard differentiable functional defined on the space D[0,1] × D[0,1]. Such differentiability property of the estimator leads to its linear approximation in a straightforward way. Thereby, the asymptotic normality of the estimator is derived under less stringent conditions

Keywords:

• Asymptotic normality
• Hadamard differentiability
• L-estimation
• linear models
• statistical functional
• weighted empirical processes