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Robust doubly protected estimators for quantiles with missing data

Author

Listed:
  • Mariela Sued

    (Universidad de Buenos Aires and CONICET)

  • Marina Valdora

    (Universidad de Buenos Aires)

  • Víctor Yohai

    (Universidad de Buenos Aires and CONICET)

Abstract

Doubly protected methods are widely used for estimating the population mean of an outcome Y from a sample where the response is missing in some individuals. To compensate for the missing responses, a vector $$\mathbf {X}$$ X of covariates is observed at each individual, and the missing mechanism is assumed to be independent of the response, conditioned on $$\mathbf {X}$$ X (missing at random). In recent years, many authors have turned from the estimation of the mean to that of the median, and more generally, doubly protected estimators of the quantiles have been proposed. In this work, we present doubly protected estimators for the quantiles in semiparametric models that are also robust, in the sense that they are resistant to the presence of outliers in the sample.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:3:d:10.1007_s11749-019-00689-9
    DOI: 10.1007/s11749-019-00689-9
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    References listed on IDEAS

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    1. 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.
    2. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    3. Porter Kristin E. & Gruber Susan & van der Laan Mark J. & Sekhon Jasjeet S., 2011. "The Relative Performance of Targeted Maximum Likelihood Estimators," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-34, August.
    4. 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.
    5. Ana M. Bianco & Paula M. Spano, 2019. "Robust inference for nonlinear regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 369-398, June.
    6. Boente, Graciela & Fraiman, Ricardo, 1989. "Robust nonparametric regression estimation," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 180-198, May.
    7. Graciela Boente & Daniela Rodriguez, 2012. "Robust estimates in generalized partially linear single-index models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 386-411, June.
    8. Zhiwei Zhang & Zhen Chen & James F. Troendle & Jun Zhang, 2012. "Causal Inference on Quantiles with an Obstetric Application," Biometrics, The International Biometric Society, vol. 68(3), pages 697-706, September.
    9. Boente, Graciela & Rodriguez, Daniela, 2008. "Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2808-2828, January.
    10. Florencia Statti & Mariela Sued & Victor J. Yohai, 2018. "High breakdown point robust estimators with missing data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(21), pages 5145-5162, November.
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