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A unified framework of constrained regression

机译：约束回归的统一框架

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Generalized additive models (GAMs) play an important role in modeling and understanding complex relationships in modern applied statistics. They allow for flexible, data-driven estimation of covariate effects. Yet researchers often have a priori knowledge of certain effects, which might be monotonic or periodic (cyclic) or should fulfill boundary conditions. We propose a unified framework to incorporate these constraints for both univariate and bivariate effect estimates and for varying coefficients. As the framework is based on component-wise boosting methods, variables can be selected intrinsically, and effects can be estimated for a wide range of different distributional assumptions. Bootstrap confidence intervals for the effect estimates are derived to assess the models. We present three case studies from environmental sciences to illustrate the proposed seamless modeling framework. All discussed constrained effect estimates are implemented in the comprehensive R package mboost for model-based boosting.
机译：广义加性模型（GAM）在建模和理解现代应用统计中的复杂关系中起着重要作用。它们允许对协变量效应进行灵活的，数据驱动的估计。然而，研究人员通常对某些影响具有先验知识，这些影响可能是单调的或周期性的（循环的）或应满足边界条件。我们提出了一个统一的框架，以将这些约束纳入单变量和双变量效应估计以及变化的系数中。由于该框架基于逐件增强方法，因此可以从本质上选择变量，并且可以针对各种不同的分布假设估算效果。得出影响估计的自举置信区间以评估模型。我们提供了来自环境科学的三个案例研究，以说明所提出的无缝建模框架。所有讨论的约束效果估计都在综合R包mboost中实现，用于基于模型的增强。

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