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Non‐parametric small area models using shape‐constrained penalized B ‐splines
Author(s) -
Wagner Julian,
Münnich Ralf,
Hill Joachim,
Stoffels Johannes,
Udelhoven Thomas
Publication year - 2017
Publication title -
journal of the royal statistical society: series a (statistics in society)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.103
H-Index - 84
eISSN - 1467-985X
pISSN - 0964-1998
DOI - 10.1111/rssa.12295
Subject(s) - estimator , spline (mechanical) , estimation , parametric statistics , mathematics , small area estimation , canopy , quadratic equation , mathematical optimization , statistics , computer science , econometrics , geography , engineering , geometry , structural engineering , systems engineering , archaeology
Summary 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.