Abstract
<abstract><p>We study the varying-coefficient partially linear model when some linear covariates are not observed, but their auxiliary instrumental variables are available. Combining the calibrated error-prone covariates and modal regression, we present a two-stage efficient estimation procedure, which is robust against outliers or heavy-tail error distributions. Asymptotic properties of the resulting estimators are established. Performance of our proposed estimation procedure is illustrated through some numerous simulations and a real example. And the results confirm that the proposed methods are satisfactory.</p></abstract>
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