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.Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 11 is March 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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根据定量平滑度约束定义的参数模型或非参数模型的有价值的替代方案。虽然后两类模型通常难以先验地证明其合理性，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、适应性、形状约束曲线的诚实置信带以及分布回归，即在给定特定条件下推断实值响应的条件分布。 《统计及其应用年度回顾》第 11 卷的预计最终在线发布日期为 2024 年 3 月。请参阅 http://www.annualreviews.org/page/journal/pubdates 了解修订后的估计。