European Journal of Forest Research

, Volume 131, Issue 5, pp 1313–1326

Testing copula regression against benchmark models for point and interval estimation of tree wood volume in beech stands


    • School of Civil Engineering and GeosciencesNewcastle University
    • Willis Research Network
  • Salvatore Grimaldi
    • Dipartimento DIBAFUniversità della Tuscia
    • Honors Center of Italian Universities, H2CU, Sapienza Università di Roma
    • Department of Mechanical and Aerospace EngineeringPolytechnic Institute of New York University, Six MetroTech Center
  • Mohammad Abdolhosseini
    • Department of Water EngineeringCollege of Agriculture, Isfahan University of Technology
  • Piermaria Corona
    • Dipartimento DIBAFUniversità della Tuscia
  • Dora Cimini
    • Dipartimento DIBAFUniversità della Tuscia
Original Paper

DOI: 10.1007/s10342-012-0600-2

Cite this article as:
Serinaldi, F., Grimaldi, S., Abdolhosseini, M. et al. Eur J Forest Res (2012) 131: 1313. doi:10.1007/s10342-012-0600-2


This study compares copula regression, recently introduced in the forest biometric literature, with four benchmark regression models for computing wood volume V in forest stands given the values of diameter at breast height D and total height H, and suggests a set of statistical techniques for the accurate assessment of model performance. Two regression models deduced from the trivariate copula-based distribution of VD, and H are tested against the classical Spurr’s model and Schumacher-Hall’s model based on allometric and geometric concepts, and two regression models that rely on Box-Cox transformed variables and are in a middle ground, in terms of model complexity, between copula-based regression and classical models. The accuracy of the point estimates of V is assessed by a suitable set of performance criteria and the nonparametric sign test, whereas the associated uncertainty is evaluated by comparing empirical and nominal coverage probabilities of the prediction intervals. Focusing on point estimates, the Schumacher-Hall’s model outperforms the other models in terms of several performance criteria. The sign test points out that the differences among the models that involve D and H as separate covariates are not definitely significant, whereas these models outperform the models with a single covariate. As far as the interval estimates are of concern, the four benchmark models provide comparable interval estimates. The copula-based model with parametric marginals is definitely outperformed by its competitors according to all criteria, whereas the copula-based model with nonparametric marginals provides quite accurate point estimates but biased interval estimates of V.


Fagus sylvaticaWeighted regressionBox-Cox transformationCopula regressionNormal quantile transformationUncertainty

Copyright information

© Springer-Verlag 2012