Deconvolution-based score tests in measurement error models. (English) Zbl 0724.62070

Stefanski, Leonard A.; Carroll, Raymond J.

Ann. Stat. 19, No. 1, 249-259 (1991).

Summary: 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 \(m(w)=E(X| W=w)\) 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.

MSC:

62J12	Generalized linear models (logistic models)
62G07	Density estimation

Keywords:

deconvolution; density estimation; empirical Bayes; errors-in-variables; maximum likelihood; generalized linear model; measurement error; efficient score test; absence of association; asymptotically efficient tests; Rates of convergence