Deconvolution-Based Score Tests in Measurement Error Models

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.