Semiparametric estimators of functional measurement error models with unknown error

Peter Hall and Yanyuan Ma

Journal of the Royal Statistical Society Series B, 2007, vol. 69, issue 3, 429-446

Abstract: Summary. We consider functional measurement error models where the measurement error distribution is estimated non‐parametrically. We derive a locally efficient semiparametric estimator but propose not to implement it owing to its numerical complexity. Instead, a plug‐in estimator is proposed, where the measurement error distribution is estimated through non‐parametric kernel methods based on multiple measurements. The root n consistency and asymptotic normality of the plug‐in estimator are derived. Despite the theoretical inefficiency of the plug‐in estimator, simulations demonstrate its near optimal performance. Computational advantages relative to the theoretically efficient estimator make the plug‐in estimator practically appealing. Application of the estimator is illustrated by using the Framingham data example.

Date: 2007
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