Statistical models defined by shape constraints are a valuable alternative to parametric models or nonparametric models defined in terms of quantitative smoothness constraints. While the latter two classes of models are typically difficult to justify a priori, many applications involve natural shape constraints, for instance, monotonicity of a density or regression function. We review some of the history of this subject and recent developments, with special emphasis on algorithmic aspects, adaptivity, honest confidence bands for shape-constrained curves, and distributional regression, i.e., inference about the conditional distribution of a real-valued response given certain covariates.

中文翻译：

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形状约束统计推断


由形状约束定义的统计模型是参数模型或根据定量平滑度约束定义的非参数模型的有价值的替代方案。虽然后两类模型通常很难先验证明，但许多应用涉及自然形状约束，例如密度或回归函数的单调性。我们回顾了该主题的一些历史和最近的发展，特别强调算法方面、自适应性、形状约束曲线的诚实置信带和分布回归，即推断给定某些协变量的实值响应的条件分布。