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.
Publié le : 1978-05-14
Classification:
Estimation,
confidence interval,
linear regression,
efficiency,
62G05,
62G15,
62G20,
62J05,
62G35
@article{1176344204,
author = {Scholz, Friedrich-Wilhelm},
title = {Weighted Median Regression Estimates},
journal = {Ann. Statist.},
volume = {6},
number = {1},
year = {1978},
pages = { 603-609},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344204}
}
Scholz, Friedrich-Wilhelm. Weighted Median Regression Estimates. Ann. Statist., Tome 6 (1978) no. 1, pp. 603-609. http://gdmltest.u-ga.fr/item/1176344204/