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Non‐parametric small area estimation using penalized spline regression

Author

Listed:
  • J. D. Opsomer
  • G. Claeskens
  • M. G. Ranalli
  • G. Kauermann
  • F. J. Breidt

Abstract

Summary. The paper proposes a small area estimation approach that combines small area random effects with a smooth, non‐parametrically specified trend. By using penalized splines as the representation for the non‐parametric trend, it is possible to express the non‐parametric small area estimation problem as a mixed effect model regression. The resulting model is readily fitted by using existing model fitting approaches such as restricted maximum likelihood. We present theoretical results on the prediction mean‐squared error of the estimator proposed and on likelihood ratio tests for random effects, and we propose a simple non‐parametric bootstrap approach for model inference and estimation of the small area prediction mean‐squared error. The applicability of the method is demonstrated on a survey of lakes in north‐eastern USA.

Suggested Citation

  • J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
    • Handle: RePEc:bla:jorssb:v:70:y:2008:i:1:p:265-286
    DOI: 10.1111/j.1467-9868.2007.00635.x
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    References listed on IDEAS

    as
    1. Gerda Claeskens, 2004. "Restricted likelihood ratio lack‐of‐fit tests using mixed spline models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 909-926, November.
    2. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    4. Helen Parise & M. P. Wand & David Ruppert & Louise Ryan, 2001. "Incorporation of historical controls using semiparametric mixed models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(1), pages 31-42.
    5. Brent A. Coull & David Ruppert & M. P. Wand, 2001. "Simple Incorporation of Interactions into Additive Models," Biometrics, The International Biometric Society, vol. 57(2), pages 539-545, June.
    6. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    7. Ciprian Crainiceanu & David Ruppert & Gerda Claeskens & M. P. Wand, 2005. "Exact likelihood ratio tests for penalised splines," Biometrika, Biometrika Trust, vol. 92(1), pages 91-103, March.
    8. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    9. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    10. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
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