ERRORS-IN-COVARIATES EFFECT ON ESTIMATING FUNCTIONS: ADDITIVITY IN LIMIT AND NONPARAMETRIC CORRECTION

We consider Poisson, logistic and Cox regressions when some covariates are not accurately ascertainable but contaminated with additive errors. Huang and Wang (1999, 2000, 2001) showed that the slope parameters can be consistently esti- mated via nonparametric correction, without imposing distributional assumptions on both the underlying true covariates and the errors. However, certain instrumen- tal variables, particularly replicated error-contaminated covariates, are required. In this article, we discover that the error eect is additive in the limit on some properly formulated estimating functions. This nding gives rise to a new nonparametric correction technique that accommodates a broad variety of practically important, internal and external error-assessment data. Simulations for Cox regression with external reliability data are conducted, and the application to an AIDS study is presented as an illustration.

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