| Abstract: | 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 l W = w) which is generally unknown (Tosteson and Tsiatis, 1988). 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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