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Annual Review of Statistics and Its Application

Volume 11, 2024

Shape-Constrained Statistical Inference

Abstract

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.

Keyword(s): adaptivity, convexity, distributional regression, honest confidence region, log-concavity, monotonicity, regression quantile
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/content/journals/10.1146/annurev-statistics-033021-014937
2024-04-22
2025-04-23
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/content/journals/10.1146/annurev-statistics-033021-014937
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Shape-Constrained Statistical Inference
Annual Review of Statistics and Its Application 11, 373 (2024); https://doi.org/10.1146/annurev-statistics-033021-014937
/content/journals/10.1146/annurev-statistics-033021-014937
/content/journals/10.1146/annurev-statistics-033021-014937
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