## The Annals of Statistics

### Adaptive $L$-Estimation for Linear Models

#### Abstract

Asymptotically efficient (adaptive) estimators for the slope parameters of the linear regression model are constructed based upon the "regression quantile" statistics suggested by Koenker and Bassett. The estimators are natural analogues of the adaptive $L$-estimators of location of Sacks, but employ kernel-density type estimators of the optimal $L$-estimator weight function.

#### Article information

Source
Ann. Statist., Volume 17, Number 1 (1989), 362-381.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176347022

Digital Object Identifier
doi:10.1214/aos/1176347022

Mathematical Reviews number (MathSciNet)
MR981456

Zentralblatt MATH identifier
0736.62060

JSTOR
Portnoy, Stephen; Koenker, Roger. Adaptive $L$-Estimation for Linear Models. Ann. Statist. 17 (1989), no. 1, 362--381. doi:10.1214/aos/1176347022. https://projecteuclid.org/euclid.aos/1176347022
• See Correction: Stephen Portnoy, Roger Koenker. Correction: Adaptive $L$-Estimation for Linear Models. Ann. Statist., Volume 18, Number 2 (1990), 986--986.