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Small area estimation using a nonparametric model-based direct estimator

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  • Salvati, Nicola
  • Chandra, Hukum
  • Giovanna Ranalli, M.
  • Chambers, Ray
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    Abstract

    Nonparametric regression is widely used as a method of characterizing a non-linear relationship between a variable of interest and a set of covariates. Practical application of nonparametric regression methods in the field of small area estimation is fairly recent, and has so far focussed on the use of empirical best linear unbiased prediction under a model that combines a penalized spline (p-spline) fit and random area effects. The concept of model-based direct estimation is used to develop an alternative nonparametric approach to estimation of a small area mean. The suggested estimator is a weighted average of the sample values from the area, with weights derived from a linear regression model with random area effects extended to incorporate a smooth, nonparametrically specified trend. Estimation of the mean squared error of the proposed small area estimator is also discussed. Monte Carlo simulations based on both simulated and real datasets show that the proposed model-based direct estimator and its associated mean squared error estimator perform well. They are worth considering in small area estimation applications where the underlying population regression relationships are non-linear or have a complicated functional form.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 54 (2010)
    Issue (Month): 9 (September)
    Pages: 2159-2171

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    Handle: RePEc:eee:csdana:v:54:y:2010:i:9:p:2159-2171

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    Web page: http://www.elsevier.com/locate/csda

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    Keywords: Non-linear regression model Empirical best linear unbiased prediction Penalized splines Mean squared error estimator Unit level model;

    References

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    1. Ugarte, M.D. & Goicoa, T. & Militino, A.F. & Durbán, M., 2009. "Spline smoothing in small area trend estimation and forecasting," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3616-3629, August.
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, April.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, April.
    4. María José Lombardía & Stefan Sperlich, 2008. "Semiparametric inference in generalized mixed effects models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 913-930.
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    Cited by:
    1. Stefan Sperlich, 2013. "Comments on: Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(2), pages 227-233, June.
    2. Chiara Bocci & Emilia Rocco, 2014. "Estimates for geographical domains through geoadditive models in presence of incomplete geographical information," Statistical Methods and Applications, Springer, vol. 23(2), pages 283-305, June.
    3. N. Salvati & N. Tzavidis & M. Pratesi & R. Chambers, 2012. "Small area estimation via M-quantile geographically weighted regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 21(1), pages 1-28, March.

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