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A note on kernel assisted estimators in missing covariate regression

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  • Wang, Suojin
  • Wang, C. Y.

Abstract

We investigate the asymptotic relationships among three kernel assisted semiparametric estimators in regression analysis when some covariates are missing or measured with error. Smoothing techniques are employed in estimating the selection probabilities and the conditionally expected scores, a step which is required to obtain the estimators of interest. The asymptotic distributional properties of these estimators are derived and their asymptotic equivalence is shown. Some important differences are also noted. Furthermore, the asymptotic efficiency of the estimators relative to the usual maximum likelihood estimator is obtained.

Suggested Citation

  • Wang, Suojin & Wang, C. Y., 2001. "A note on kernel assisted estimators in missing covariate regression," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 439-449, December.
    • Handle: RePEc:eee:stapro:v:55:y:2001:i:4:p:439-449
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    References listed on IDEAS

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    1. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
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    1. Fayyaz Bahari & Safar Parsi & Mojtaba Ganjali, 2021. "Empirical likelihood inference in general linear model with missing values in response and covariates by MNAR mechanism," Statistical Papers, Springer, vol. 62(2), pages 591-622, April.
    2. Lei Jin & Suojin Wang, 2010. "A Model Validation Procedure when Covariate Data are Missing at Random," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 403-421, September.
    3. Creemers, An & Aerts, Marc & Hens, Niel & Molenberghs, Geert, 2012. "A nonparametric approach to weighted estimating equations for regression analysis with missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 100-113, January.
    4. Lihong Qi & Xu Zhang & Yanqing Sun & Lu Wang & Yichuan Zhao, 2019. "Weighted estimating equations for additive hazards models with missing covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 365-387, April.
    5. Qiu, Zhiping & Chen, Xiaoping & Zhou, Yong, 2015. "A kernel-assisted imputation estimating method for the additive hazards model with missing censoring indicator," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 89-97.
    6. Lukusa, Martin T. & Phoa, Frederick Kin Hing, 2020. "A note on the weighting-type estimations of the zero-inflated Poisson regression model with missing data in covariates," Statistics & Probability Letters, Elsevier, vol. 158(C).
    7. Menggang Yu & Bin Nan, 2010. "Regression Calibration in Semiparametric Accelerated Failure Time Models," Biometrics, The International Biometric Society, vol. 66(2), pages 405-414, June.
    8. Fayyaz Bahari & Safar Parsi & Mojtaba Ganjali, 2021. "Goodness of fit test for general linear model with nonignorable missing on response variable," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 163-196, March.
    9. Na Hu & Xuerong Chen & Jianguo Sun, 2015. "Regression Analysis of Length-biased and Right-censored Failure Time Data with Missing Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 438-452, June.
    10. Shen-Ming Lee & T. Martin Lukusa & Chin-Shang Li, 2020. "Estimation of a zero-inflated Poisson regression model with missing covariates via nonparametric multiple imputation methods," Computational Statistics, Springer, vol. 35(2), pages 725-754, June.
    11. T. Martin Lukusa & Shen-Ming Lee & Chin-Shang Li, 2016. "Semiparametric estimation of a zero-inflated Poisson regression model with missing covariates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(4), pages 457-483, May.
    12. Zhuoer Sun & Suojin Wang, 2019. "Semiparametric estimation in regression with missing covariates using single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1201-1232, October.
    13. Huijuan Ma & Limin Peng & Zhumin Zhang & HuiChuan J. Lai, 2018. "Generalized accelerated recurrence time model for multivariate recurrent event data with missing event type," Biometrics, The International Biometric Society, vol. 74(3), pages 954-965, September.

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