Nonparametric Shape-Restricted Regression

By Adityanand Guntuboyina, Bodhisattva Sen. Statistical Science, 2017

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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 shape-restricted 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 risk behavior 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 shape-restricted functions. We also briefly discuss the computation of the LSE and indicate some open research problems and future directions.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7de50ca35b8ee85fc72e602d97c4c4afa21130b7

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Citations in the corpus

Regression diagnostics meets forecast evaluation: conditional calibration, reliability diagrams, and coefficient of determination (2021, background): “…Dümbgen (2020) establish rates of uniform convergence in the cases of threshold (non) exceedance and quantile functionals that complement classical theory (Barlow et al., 1972; Casady and Cryer, 1976; Wright, 1984; Robertson et al., 1988; El Barmi and Mukerjee, 2005; Guntuboyina and Sen, 2018).”