Shape-Constrained Statistical Inference

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...

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Bibliographic Details
Published inAnnual review of statistics and its application Vol. 11; no. 1; pp. 373 - 391
Main Author Dümbgen, Lutz
Format Journal Article
LanguageEnglish
Published Annual Reviews 22.04.2024
Subjects
adaptivity
convexity
distributional regression
honest confidence region
log-concavity
monotonicity
regression quantile
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Summary: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.
ISSN:2326-8298
2326-831X
DOI:10.1146/annurev-statistics-033021-014937