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Semiparametric estimators of functional measurement error models with unknown error

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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.

Keywords: Errors in variables; Latent variables; Measurement error; Semiparametric efficiency; Semiparametric methods

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2007.00596.x

Affiliations: 1: Australian National University, Canberra, Australia 2: Texas A&M University, College Station, USA

Publication date: June 1, 2007

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