Abstract
We consider the consistency and weak convergence of $S$-estimators in the linear regression model. Sufficient conditions for consistency with varying dimension are given which are sufficiently weak to cover, for example, polynomial trends and i.i.d. carriers. A weak convergence theorem for the Hampel-Rousseeuw least median of squares estimator is obtained, and it is shown under rather general conditions that the correct norming factor is $n^{1/3}$. Finally, the asymptotic normality of $S$-estimators with a smooth $\rho$-function is obtained again under weak conditions on the carriers.
Citation
Laurie Davies. "The Asymptotics of $S$-Estimators in the Linear Regression Model." Ann. Statist. 18 (4) 1651 - 1675, December, 1990. https://doi.org/10.1214/aos/1176347871
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