Asymptotic Behavior of Robust Estimators of Regression and Scale Parameters with Fixed Carriers
Asymptotic Behavior of Robust Estimators of Regression and Scale Parameters with Fixed Carriers
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.