Nonparametric Shape-Restricted Regression

• Autores: Adityanand Guntuboyina, Bodhisattva Sen
• Localización: Statistical science, ISSN 0883-4237, Vol. 33, Nº. Extra 4, 2018 (Ejemplar dedicado a: Nonparametric Inference Under Shape Constraints), págs. 568-594
• Idioma: inglés
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• Resumen

  • We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shaperestricted regression and constrained single index model. We review some of the theoretical properties of the least squares estimator (LSE) in these problems, emphasizing on the adaptive nature of the LSE. In particular, we study the behavior of the risk of the LSE, and its pointwise limiting distribution theory, with special emphasis to isotonic regression. We survey various methods for constructing pointwise confidence intervals around these shaperestricted functions. We also briefly discuss the computation of the LSE and indicate some open research problems and future directions.