For the linear regression model, $y_i = \mathbf{x}_i\mathbf{\beta} + \varepsilon_i$ with fixed $\mathbf{x}_i s$, the asymptotic normality of $(\hat{\mathbf{\beta}}, \hat{\sigma})$ which minimizes the Huber-Dutter loss function, $\sum\sigma\rho\{(y_i - \mathbf{x}_i\mathbf{\beta})/\sigma\} + A_n\sigma$, is established under rather general conditions.
Publié le : 1985-12-14
Classification:
Linear regression,
robust estimation,
$M$ estimator,
simultaneous scale estimation,
62J05,
62F35,
62F11,
62F12
@article{1176349750,
author = {Silvapulle, Mervyn J.},
title = {Asymptotic Behavior of Robust Estimators of Regression and Scale Parameters with Fixed Carriers},
journal = {Ann. Statist.},
volume = {13},
number = {1},
year = {1985},
pages = { 1490-1497},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349750}
}
Silvapulle, Mervyn J. Asymptotic Behavior of Robust Estimators of Regression and Scale Parameters with Fixed Carriers. Ann. Statist., Tome 13 (1985) no. 1, pp. 1490-1497. http://gdmltest.u-ga.fr/item/1176349750/