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Non‐parametric small area models using shape‐constrained penalized B‐splines

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  • Julian Wagner
  • Ralf Münnich
  • Joachim Hill
  • Johannes Stoffels
  • Thomas Udelhoven

Abstract

For the estimation of spruce timber reserves in individual forest districts of the German federal state Rhineland‐Palatinate, small area methods are applied. A model using stock values of the state forest inventory and a canopy height model derived by airborne laser scanning is used to provide adequate estimates. Since the interaction between the variables is non‐linear and must fulfil further constraints, a new spline‐based small area estimation method is proposed, formulated as a quadratic programming problem. This method enables providing realistic estimates via including specialized constraints which are especially important in practice as well as more stable estimates. The applicability of the new method and the related mean‐squared‐error estimators is shown in a simulation study. Further, spruce timber reserves in Rhineland‐Palatinate are estimated by using the new approach compared with already existing methods.

Suggested Citation

  • Julian Wagner & Ralf Münnich & Joachim Hill & Johannes Stoffels & Thomas Udelhoven, 2017. "Non‐parametric small area models using shape‐constrained penalized B‐splines," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1089-1109, October.
    • Handle: RePEc:bla:jorssa:v:180:y:2017:i:4:p:1089-1109
    DOI: 10.1111/rssa.12295
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    References listed on IDEAS

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    1. Opsomer, Jean D. & Breidt, F. Jay & Moisen, Gretchen G. & Kauermann, Goran, 2007. "Model-Assisted Estimation of Forest Resources With Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 400-409, June.
    2. 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.
    3. McDonald, G. T. & Lane, M. B., 2004. "Converging global indicators for sustainable forest management," Forest Policy and Economics, Elsevier, vol. 6(1), pages 63-70, January.
    4. 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.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    6. F. J. Breidt & G. Claeskens & J. D. Opsomer, 2005. "Model-assisted estimation for complex surveys using penalised splines," Biometrika, Biometrika Trust, vol. 92(4), pages 831-846, December.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
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    Cited by:

    1. Jan Pablo Burgard & Patricia Dörr & Ralf Münnich, 2020. "Monte-Carlo Simulation Studies in Survey Statistics – An Appraisal," Research Papers in Economics 2020-04, University of Trier, Department of Economics.
    2. María José Lombardía & Esther López-Vizcaíno & Cristina Rueda, 2021. "Selection model for domains across time: application to labour force survey by economic activities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 228-254, March.

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