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Locally efficient estimation in generalized partially linear model with measurement error in nonlinear function

Author

Listed:
  • Qianqian Wang

    (University of South Carolina)

  • Yanyuan Ma

    (Pennsylvania State University)

  • Guangren Yang

    (Jinan University)

Abstract

We investigate the errors in covariates issues in a generalized partially linear model. Different from the usual literature (Ma and Carroll in J Am Stat Assoc 101:1465–1474, 2006), we consider the case where the measurement error occurs to the covariate that enters the model nonparametrically, while the covariates precisely observed enter the model parametrically. To avoid the deconvolution type operations, which can suffer from very low convergence rate, we use the B-splines representation to approximate the nonparametric function and convert the problem into a parametric form for operational purpose. We then use a parametric working model to replace the distribution of the unobservable variable, and devise an estimating equation to estimate both the model parameters and the functional dependence of the response on the latent variable. The estimation procedure is devised under the functional model framework without assuming any distribution structure of the latent variable. We further derive theories on the large sample properties of our estimator. Numerical simulation studies are carried out to evaluate the finite sample performance, and the practical performance of the method is illustrated through a data example.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:2:d:10.1007_s11749-019-00668-0
    DOI: 10.1007/s11749-019-00668-0
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    References listed on IDEAS

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    1. 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.
    2. Liu, Lian, 2007. "Estimation of generalized partially linear models with measurement error using sufficiency scores," Statistics & Probability Letters, Elsevier, vol. 77(15), pages 1580-1588, September.
    3. 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.
    4. 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.
    5. Carroll, R.J. & Fan, Jianqing. & Gijbels, Irene. & Wand, M.P., "undated". "Generalized Partially Linear Single-Index Models," Statistics Working Paper 95010, Australian Graduate School of Management.
    6. Ma, Yanyuan & Carroll, Raymond J., 2006. "Locally Efficient Estimators for Semiparametric Models With Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1465-1474, December.
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