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Locally efficient semiparametric estimators for functional measurement error models

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  • Anastasios A. Tsiatis
  • Yanyuan Ma

Abstract

A class of semiparametric estimators are proposed in the general setting of functional measurement error models. The estimators follow from estimating equations that are based on the semiparametric efficient score derived under a possibly incorrect distributional assumption for the unobserved 'measured with error' covariates. It is shown that such estimators are consistent and asymptotically normal even with misspecification and are efficient if computed under the truth. The methods are demonstrated with a simulation study of a quadratic logistic regression model with measurement error. Copyright 2004, Oxford University Press.

Suggested Citation

  • Anastasios A. Tsiatis & Yanyuan Ma, 2004. "Locally efficient semiparametric estimators for functional measurement error models," Biometrika, Biometrika Trust, vol. 91(4), pages 835-848, December.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:4:p:835-848
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    File URL: http://hdl.handle.net/10.1093/biomet/91.4.835
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    Cited by:

    1. Stoklosa, Jakub & Huang, Yih-Huei & Furlan, Elise & Hwang, Wen-Han, 2016. "On quadratic logistic regression models when predictor variables are subject to measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 109-121.
    2. Tanya P. Garcia & Yanyuan Ma, 2016. "Optimal Estimator for Logistic Model with Distribution-free Random Intercept," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 156-171, March.
    3. Yanyuan Ma & Marc G. Genton, 2010. "Explicit estimating equations for semiparametric generalized linear latent variable models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 475-495, September.
    4. 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.
    5. 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.
    6. 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.
    7. Yuedong Wang & Yanyuan Ma & Raymond J. Carroll, 2009. "Variance estimation in the analysis of microarray data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 425-445, April.
    8. Liang, Liang & Ma, Yanyuan & Carroll, Raymond J., 2019. "A semiparametric efficient estimator in case-control studies for gene–environment independent models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 38-50.
    9. Li, Mengyan & Ma, Yanyuan & Li, Runze, 2019. "Semiparametric regression for measurement error model with heteroscedastic error," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 320-338.
    10. Kun Xu & Yanyuan Ma & Liqun Wang, 2015. "Instrument Assisted Regression for Errors in Variables Models with Binary Response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 104-117, March.
    11. Fei Jiang & Sebastien Haneuse, 2017. "A Semi-parametric Transformation Frailty Model for Semi-competing Risks Survival Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 112-129, March.
    12. Bo Zhang & Eric J. Tchetgen Tchetgen, 2022. "A semi‐parametric approach to model‐based sensitivity analysis in observational studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 668-691, December.
    13. Yuanjia Wang & Tanya P. Garcia & Yanyuan Ma, 2012. "Nonparametric Estimation for Censored Mixture Data With Application to the Cooperative Huntington’s Observational Research Trial," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1324-1338, December.
    14. Roberto Mari & Antonello Maruotti, 2022. "A two-step estimator for generalized linear models for longitudinal data with time-varying measurement error," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 273-300, June.
    15. Qianqian Wang & Yanyuan Ma & Guangren Yang, 2020. "Locally efficient estimation in generalized partially linear model with measurement error in nonlinear function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 553-572, June.
    16. Yuhang Xu & Yehua Li & Xiao Song, 2016. "Locally Efficient Semiparametric Estimators for Proportional Hazards Models with Measurement Error," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 558-572, June.
    17. 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.
    18. Mijeong Kim & Yanyuan Ma, 2012. "The efficiency of the second-order nonlinear least squares estimator and its extension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 751-764, August.
    19. Paola Berchialla & Veronica Sciannameo & Sara Urru & Corrado Lanera & Danila Azzolina & Dario Gregori & Ileana Baldi, 2021. "Adjustment for Baseline Covariates to Increase Efficiency in RCTs with Binary Endpoint: A Comparison of Bayesian and Frequentist Approaches," IJERPH, MDPI, vol. 18(15), pages 1-9, July.

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