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

• Published in: Journal of the Royal Statistical Society. Series A, Statistics in society Statistics in society, 2017-10, Vol.180 (4), p.1089-1109
• Main Authors: Wagner, Julian, Münnich, Ralf, Hill, Joachim, Stoffels, Johannes, Udelhoven, Thomas
• Format: Article
• Language: English
• Subjects: Airborne lasers; Canopies; Computer simulation; Estimates; Forests; Nonparametric statistics; Quadratic programming; Regional estimation; Remote sensing data; Reserves; Shape‐constrained spline models; Simulation; Splines
• ISSN: 0964-1998; 1467-985X
• DOI: 10.1111/rssa.12295

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 meansquared-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.