Abstract:
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We consider generalized linear models (GLM) that are widely used in medicine, social sciences, business applications, and other areas. For these models, real data analysis often brings in covariates that are measured with errors or not observed directly. Likelihood methods and moments based methods are the two main approaches for statistical estimation and inference in these models. The method of moments provides feasible alternatives to the likelihood approach when the likelihood function involves multiple integrals which do not have closed forms. This method does not require parametric assumptions for the distribution of the unobserved covariates and error components. We present a simulation-based method-of-moments approach for constructing estimators for unknown parameters of GLM's with categorical response variables and mismeasured covariates. We prove consistency and asymptotically normality of the obtained estimators under some regularity conditions, and illustrate our estimation approach through simulation studies.
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