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Semiparametric estimators of functional measurement error models with unknown error

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  • Peter Hall
  • Yanyuan Ma

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.

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  • Peter Hall & Yanyuan Ma, 2007. "Semiparametric estimators of functional measurement error models with unknown error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 429-446, June.
    • Handle: RePEc:bla:jorssb:v:69:y:2007:i:3:p:429-446
    DOI: 10.1111/j.1467-9868.2007.00596.x
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    Cited by:

    1. Aurore Delaigle & Peter Hall, 2016. "Methodology for non-parametric deconvolution when the error distribution is unknown," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 231-252, January.
    2. Dong, Hao & Taylor, Luke, 2022. "Nonparametric Significance Testing In Measurement Error Models," Econometric Theory, Cambridge University Press, vol. 38(3), pages 454-496, June.
    3. Li, Mengyan & Li, Runze & Ma, Yanyuan, 2021. "Inference in high dimensional linear measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    4. Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.
    5. Garcia, Tanya P. & Ma, Yanyuan, 2017. "Simultaneous treatment of unspecified heteroskedastic model error distribution and mismeasured covariates for restricted moment models," Journal of Econometrics, Elsevier, vol. 200(2), pages 194-206.
    6. Jun Zhang & Zhenghui Feng & Peirong Xu & Hua Liang, 2017. "Generalized varying coefficient partially linear measurement errors models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 97-120, February.
    7. Yanyuan Ma & Jeffrey D. Hart & Ryan Janicki & Raymond J. Carroll, 2011. "Local and omnibus goodness‐of‐fit tests in classical measurement error models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 81-98, January.
    8. Grace Y. Yi & Yanyuan Ma & Donna Spiegelman & Raymond J. Carroll, 2015. "Functional and Structural Methods With Mixed Measurement Error and Misclassification in Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 681-696, June.
    9. Samiran Sinha & Yanyuan Ma, 2014. "Semiparametric analysis of linear transformation models with covariate measurement errors," Biometrics, The International Biometric Society, vol. 70(1), pages 21-32, March.

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