Open Access
Translator Disclaimer
May, 1978 Weighted Median Regression Estimates
Friedrich-Wilhelm Scholz
Ann. Statist. 6(3): 603-609 (May, 1978). DOI: 10.1214/aos/1176344204

Abstract

In the simple linear regression problem $\{Y_i = \alpha + \beta x_i + e_i i = 1,\cdots, n, e_i$ i.i.d. $\sim F$ continuous, $x_1 \leqq \cdots \leqq x_n$ known, $\alpha, \beta$ unknown$\}$ we investigate the following type of estimator: To each $s_{ij} = (Y_j - Y_i)/(x_j - x_i)$ with $x_i < x_j$ attach weight $w_{ij}$ and as estimator for $\beta$ consider the median of this weight distribution over the $s_{ij}$. A confidence interval for $\beta$ is found by taking certain quantiles of this weight distribution. The asymptotic behavior of both is investigated and conditions for optimal weights are given.

Citation

Download Citation

Friedrich-Wilhelm Scholz. "Weighted Median Regression Estimates." Ann. Statist. 6 (3) 603 - 609, May, 1978. https://doi.org/10.1214/aos/1176344204

Information

Published: May, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0388.62036
MathSciNet: MR468054
Digital Object Identifier: 10.1214/aos/1176344204

Subjects:
Primary: 62G05
Secondary: 62G15 , 62G20 , 62G35 , 62J05

Keywords: Confidence interval , efficiency , estimation , Linear regression

Rights: Copyright © 1978 Institute of Mathematical Statistics

JOURNAL ARTICLE
7 PAGES


SHARE
Vol.6 • No. 3 • May, 1978
Back to Top