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Estimation of the marginal location under a partially linear model with missing responses

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  • Bianco, Ana
  • Boente, Graciela
  • González-Manteiga, Wenceslao
  • Pérez-González, Ana

Abstract

In this paper, we consider a semiparametric partially linear regression model where there are missing data in the response. We propose robust Fisher-consistent estimators for the regression parameter, for the regression function and for the marginal location parameter of the response variable. A robust cross-validation method is briefly discussed, although, from our numerical results, the marginal estimators seem not to be sensitive to the bandwidth parameter. Finally, a Monte Carlo study is carried out to compare the performance of the robust proposed estimators among themselves and also with the classical ones, for normal and contaminated samples, under different missing data models. An example based on a real data set is also discussed.

Suggested Citation

  • Bianco, Ana & Boente, Graciela & González-Manteiga, Wenceslao & Pérez-González, Ana, 2010. "Estimation of the marginal location under a partially linear model with missing responses," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 546-564, February.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:546-564
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    References listed on IDEAS

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    1. Ana Bianco & Graciela Boente, 2007. "Robust estimators under semi‐parametric partly linear autoregression: Asymptotic behaviour and bandwidth selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 274-306, March.
    2. Wang, Qihua & Sun, Zhihua, 2007. "Estimation in partially linear models with missing responses at random," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1470-1493, August.
    3. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    4. Ana Bianco & Graciela Boente & Elena Martínez, 2006. "Robust Tests in Semiparametric Partly Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 435-450, September.
    5. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
    6. Marc Aerts, 2002. "Local multiple imputation," Biometrika, Biometrika Trust, vol. 89(2), pages 375-388, June.
    7. Croux, Christophe & Haesbroeck, Gentiane, 2003. "Implementing the Bianco and Yohai estimator for logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 273-295, October.
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    1. Bianco, Ana M. & Boente, Graciela & González-Manteiga, Wenceslao & Pérez-González, Ana, 2015. "Robust inference in partially linear models with missing responses," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 88-98.
    2. Ana M. Bianco & Graciela Boente & Wenceslao González-Manteiga & Ana Pérez-González, 2019. "Plug-in marginal estimation under a general regression model with missing responses and covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 106-146, March.
    3. Mariela Sued & Marina Valdora & Víctor Yohai, 2020. "Robust doubly protected estimators for quantiles with missing data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 819-843, September.

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