Abstract
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.
Citation
Mervyn J. Silvapulle. "Asymptotic Behavior of Robust Estimators of Regression and Scale Parameters with Fixed Carriers." Ann. Statist. 13 (4) 1490 - 1497, December, 1985. https://doi.org/10.1214/aos/1176349750
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