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Small area estimation based on M-quantile models in presence of outliers in auxiliary variables

Author

Listed:
  • Stefano Marchetti

    (University of Pisa)

  • Caterina Giusti

    (University of Pisa)

  • Nicola Salvati

    (University of Pisa)

  • Monica Pratesi

    (University of Pisa)

Abstract

When using small area estimation models, the presence of outlying observations in the response and/or in the auxiliary variables can severely affect the estimates of the model parameters, which can in turn affect the small area estimates produced using these models. In this paper we propose an M-quantile estimator of the small area mean that is robust to the presence of outliers in the response variable and in the continuous auxiliary variables. To estimate the variability of this estimator we propose a non-parametric bootstrap estimator. The performance of the proposed estimator is evaluated by means of model- and design-based simulations and by an application to real data. In these comparisons we also include the extension of the Robust EBLUP able to down-weight the outliers in the auxiliary variables. The results show that in the presence of outliers in the auxiliary variables the proposed estimator outperforms its traditional version that takes into account the presence of outliers only in the response variable.

Suggested Citation

  • Stefano Marchetti & Caterina Giusti & Nicola Salvati & Monica Pratesi, 2017. "Small area estimation based on M-quantile models in presence of outliers in auxiliary variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 531-555, November.
    • Handle: RePEc:spr:stmapp:v:26:y:2017:i:4:d:10.1007_s10260-017-0380-4
    DOI: 10.1007/s10260-017-0380-4
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    References listed on IDEAS

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    1. Marchetti, Stefano & Tzavidis, Nikos & Pratesi, Monica, 2012. "Non-parametric bootstrap mean squared error estimation for M-quantile estimators of small area averages, quantiles and poverty indicators," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2889-2902.
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    12. Ray Chambers & Nicola Salvati & Nikos Tzavidis, 2016. "Semiparametric small area estimation for binary outcomes with application to unemployment estimation for local authorities in the UK," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(2), pages 453-479, February.
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    1. K. Shuvo Bakar & Nicholas Biddle & Philip Kokic & Huidong Jin, 2020. "A Bayesian spatial categorical model for prediction to overlapping geographical areas in sample surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 535-563, February.

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