Penalized splines have potential to decrease estimates of variance in forest inventories with a design-based population-level inference, and a model-based domain-level inference by decreasing the likelihood of a model misspecification. We provide examples with second-order (B2) B-splines and radial basis (RB) functions as extensions to a linear working model (WM). Bias was not prominent, yet greater with B2 and in particular with RB than with WM, and decreased with sample size. Important reductions in the variance of a population mean were achieved with both B2 and RB, but at the domain-level only with RB. The proposed regression estimator of variance generated estimates of variance being slightly smaller than the observed variance. A consistent and larger underestimation was seen with the popular difference estimator of variance.

中文翻译：

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惩罚样条在森林资源调查中的种群和林分水平推断

惩罚样条线有可能通过减少模型错误指定的可能性来减少基于设计的种群水平推断和基于模型的域水平推断的森林清单方差的估计。我们提供了带有二阶（B2）B样条和径向基（RB）函数作为线性工作模型（WM）扩展的示例。偏差不显着，但B2尤其是RB的偏差大于WM，并且随着样本量的减少而减小。B2和RB均实现了总体均值方差的重要降低，但只有RB才在域级别实现了降低。拟议的方差回归估计器生成的方差估计值略小于观察到的方差。使用方差的流行差异估计量可以看到一致且较大的低估。