Shape-Constrained Statistical Inference

• Published in: Annual review of statistics and its application Vol. 11; no. 1; pp. 373 - 391
• Main Author: Dümbgen, Lutz
• Format: Journal Article
• Language: English
• Published: Annual Reviews 22.04.2024
• Subjects: adaptivity; convexity; distributional regression; honest confidence region; log-concavity; monotonicity; regression quantile
• DOI: 10.1146/annurev-statistics-033021-014937
• ISSN: 2326-8298

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.