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.
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Acknowledgements
The authors are grateful to the Associate Editor, the referee and the Editor for their helpful comments which have led to substantial improvements in the paper. The work of Salvati has been developed under the support of the project PRIN-SURWEY http://www.sp.unipg.it/surwey/ (Grant 2012F42NS8, Italy).
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Marchetti, S., Giusti, C., Salvati, N. et al. Small area estimation based on M-quantile models in presence of outliers in auxiliary variables. Stat Methods Appl 26, 531–555 (2017). https://doi.org/10.1007/s10260-017-0380-4
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DOI: https://doi.org/10.1007/s10260-017-0380-4