- Statist. Sci.
- Volume 33, Number 4 (2018), 568-594.
Nonparametric Shape-Restricted Regression
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 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 shape-restricted functions. We also briefly discuss the computation of the LSE and indicate some open research problems and future directions.
Statist. Sci., Volume 33, Number 4 (2018), 568-594.
First available in Project Euclid: 29 November 2018
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Zentralblatt MATH identifier
Adaptive risk bounds bootstrap Chernoff’s distribution convex regression isotonic regression likelihood ratio test monotone function order preserving function estimation projection on a closed convex set tangent cone
Guntuboyina, Adityanand; Sen, Bodhisattva. Nonparametric Shape-Restricted Regression. Statist. Sci. 33 (2018), no. 4, 568--594. doi:10.1214/18-STS665. https://projecteuclid.org/euclid.ss/1543482059
- Supplement to “Nonparametric Shape-Restricted Regression”. The supplement contains some of the detailed proofs of results in the paper.