Semiparametric estimators of functional measurement error models with unknown error

Peter Hall, Yanyuan Ma

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)429-446
Number of pages18
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume69
Issue number3
DOIs
StatePublished - Jun 1 2007

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Plug-in Estimator
Measurement Error Model
Estimator
Unknown
Measurement Error
Efficient Estimator
Nonparametric Methods
Kernel Methods
Asymptotic Normality
Roots
Measurement error
Semiparametric estimators
Demonstrate
Simulation

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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AB - 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.

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