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March, 1991 Deconvolution-Based Score Tests in Measurement Error Models
Leonard A. Stefanski, Raymond J. Carroll
Ann. Statist. 19(1): 249-259 (March, 1991). DOI: 10.1214/aos/1176347979


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.


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Leonard A. Stefanski. Raymond J. Carroll. "Deconvolution-Based Score Tests in Measurement Error Models." Ann. Statist. 19 (1) 249 - 259, March, 1991.


Published: March, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0724.62070
MathSciNet: MR1091848
Digital Object Identifier: 10.1214/aos/1176347979

Primary: 62J05
Secondary: 62G05 , 62H25

Keywords: Deconvolution , Density estimation , Empirical Bayes , errors-in-variables , generalized linear models , maximum likelihood , measurement error models , score tests

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 1 • March, 1991
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