Several authors have shown how to efficiently estimate $\beta$ in the semiparametric additive model $y = x'\beta + g(t) + \text{error}$, $g(t)$ smooth but unknown when the error distribution is normal. However, the general theory suggests that efficient estimation should be possible for general error distributions with finite Fisher information even when the error distribution is unknown. In this note we construct a sequence of estimators which achieves this goal under technical assumptions.
Publié le : 1992-06-14
Classification:
Semiparametric regression,
additive models,
linear models,
Hajek-Le Cam lower bound,
efficient estimators,
62G05,
62J05,
62F35
@article{1176348675,
author = {Cuzick, Jack},
title = {Efficient Estimates in Semiparametric Additive Regression Models with Unknown Error Distribution},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1129-1136},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348675}
}
Cuzick, Jack. Efficient Estimates in Semiparametric Additive Regression Models with Unknown Error Distribution. Ann. Statist., Tome 20 (1992) no. 1, pp. 1129-1136. http://gdmltest.u-ga.fr/item/1176348675/