Consider a generalized linear model with response $Y$ and scalar predictor $X$. Instead of observing $X$, a surrogate $W = X + Z$ is observed, where $Z$ represents measurement error and is independent of $X$ and $Y$. The efficient score test for the absence of association depends on $m(w) = E(X\mid W = w)$ which is generally unknown. Assuming that the distribution of $Z$ is known, asymptotically efficient tests are constructed using nonparametric estimators of $m(w)$. Rates of convergence for the estimator of $m(w)$ are established in the course of proving efficiency of the proposed test.
Publié le : 1991-03-14
Classification:
Deconvolution,
density estimation,
empirical Bayes,
errors-in-variables,
generalized linear models,
maximum likelihood,
measurement error models,
score tests,
62J05,
62H25,
62G05
@article{1176347979,
author = {Stefanski, Leonard A. and Carroll, Raymond J.},
title = {Deconvolution-Based Score Tests in Measurement Error Models},
journal = {Ann. Statist.},
volume = {19},
number = {1},
year = {1991},
pages = { 249-259},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347979}
}
Stefanski, Leonard A.; Carroll, Raymond J. Deconvolution-Based Score Tests in Measurement Error Models. Ann. Statist., Tome 19 (1991) no. 1, pp. 249-259. http://gdmltest.u-ga.fr/item/1176347979/