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Gao, Chao; Han, Fang; Zhang, Cun-Hui

On estimation of isotonic piecewise constant signals. (English) Zbl 1450.62034

Ann. Stat. 48, No. 2, 629-654 (2020).
The authors consider observing an \(n\)-dimensional vector of independent entries with unknown underlying mean. The problem solved is to derive precise minimax rates of the parametric space. They claim that this rate can be achieved by using least-squares procedures, the so-called reduced isotonic regression. They compare it with the ordinary isotonic one and prove that it can avoid overfitting the data. They also derive exact minimax rates under particular losses.
Reviewer: Carlos Narciso Bouza Herrera (Habana)

Cited in 14 Documents

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
60K35 Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

isotonic piecewise constant function; reduced isotonic regression; iterated logarithmic dependence; adaptive estimation; oracle inequalities

Software:

isotone; FDRSeg; LZeroSpikeInference
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Full Text: DOI arXiv Euclid

References:

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