Measurement Errors Regression: a Nonparametric Approach

Nonparametric regression provides a useful tool for exploring the association between the responses and covariates. In many applications, the actual values of the covariates are not known, but are measured with errors or through surrogates. In this paper, we present nonparametric regression techniques to study the association between the response and the underlying unobserved covariate. Deconvolution techniques are used to account for the errors in the covariates. The proposed regression estimators are shown to have limiting normal distributions and methods for constructing confidence intervals are also introduced. Various simulated examples based on both continuous and binary responses are included to illustrate the usefulness of the proposed methods. oAbbreviated title. Measurement errors regression AMS 1980 ,ubject clallification. Primary 62G20. Secondary 62G05, 62J99. Key word, and phrYJle,. Binary response; Confidence interval; Deconvolution; Errors-in-variables; Kernel estimator; Nonparametric regression.