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

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
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