Non-parametric Small Area Models Using Shape-Constrained PenalizedB-Splines
针对德国莱茵兰-普法尔茨州云杉木材储量估计，提出一种基于形状约束惩罚B样条的非参数小域估计方法，通过二次规划实现非线性关系建模，提供更稳定且符合实际的估计。
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.