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Yang, Fan; Barber, Rina Foygel

Contraction and uniform convergence of isotonic regression. (English) Zbl 1478.62098

Electron. J. Stat. 13, No. 1, 646-677 (2019).
Summary: We consider the problem of isotonic regression, where the underlying signal \(x\) is assumed to satisfy a monotonicity constraint, that is, \(x\) lies in the cone \(\{x\in \mathbb{R}^{n}:x_{1}\leq \dots\leq x_{n}\}\). We study the isotonic projection operator (projection to this cone), and find a necessary and sufficient condition characterizing all norms with respect to which this projection is contractive. This enables a simple and non-asymptotic analysis of the convergence properties of isotonic regression, yielding uniform confidence bands that adapt to the local Lipschitz properties of the signal.

Cited in 9 Documents

MSC:

62G08 Nonparametric regression and quantile regression
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference

Keywords:

isotonic regression; contraction; data-adaptive band; convergence rates; density estimation
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Full Text: DOI arXiv Euclid

References:

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