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Semiparametric estimators of functional measurement error models with unknown error
Author(s) -
Hall Peter,
Ma Yanyuan
Publication year - 2007
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00596.x
Subject(s) - estimator , asymptotic distribution , consistency (knowledge bases) , stein's unbiased risk estimate , efficient estimator , mathematics , consistent estimator , trimmed estimator , kernel density estimation , computer science , statistics , mathematical optimization , minimum variance unbiased estimator , artificial intelligence
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.