Abstract: 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 estimated via nonparametric correction, without imposing distributional assumptions on both the underlying true covariates and the errors. However, certain instrumental variables, particularly replicated error-contaminated covariates, are required. In this article, we discover that the error effect is additive in the limit on some properly formulated estimating functions. This finding 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.
Key words and phrases: Cox regression, external data, functional modeling, generalized linear model, logistic regression, measurement error, nonlinear model, Poisson regression, proportional hazards model, reliability study.