Risk bounds in isotonic regression

By Cun-Hui Zhang. 2002

120 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6c00e28cb079d4d871962b7df5d8c9a925d4f5ea

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In Statistics and Probability

Citations in the corpus

Nonparametric Shape-Restricted Regression (2017, background): “2 appears to be new even though its conclusion is implicit in the detailed risk calculations of [143] for isotonic regression.”
Convergence rates of least squares regression estimators with heavy-tailed errors (2017, background): “[70]) that a second moment assumption on the errors (p = 2) suffices.”
On risk bounds in isotonic and other shape restricted regression problems (2013, methodology): “The behavior of θ̂ (Y ;M), under the loss 2, has been studied in a number of papers including [6, 14, 21, 29, 30, 33, 35].”
Sharp oracle inequalities for Least Squares estimators in shape restricted regression (2015, background): “, μn) T ∈ S↑ n, it is known [13, 19, 7, 8] that for some absolute constant c > 0,”
On the Prediction Performance of the Lasso (2014, background): “Ho¨lder continuous signals. A recent review on this topic and a detailed analysis of the maximum likelihood estimator in this context can be found in [CGS13] and an earlier risk bound can be found in [Zha02]. Example 3 (Predicting monotone functions with the TV-estimator). In this example, we derive”
Isotonic regression in general dimensions (2017, methodology): “form norm. In recent years, there has been considerable interest and progress in studying the automatic rate-adaptation phenomenon of shape-constrained estimators. This line of study was pioneered by Zhang (2002) in the context of univariate isotonic regression, followed by Chatterjee, Guntuboyina a”
Optimal rates of statistical seriation (2016, methodology): “The LS estimator defined by θ̂ = argminθ∈Sn ‖θ− y‖ 2 2 can be computed in closed form in O(n) using the Pool-Adjacent-Violators algorithm (PAVA) [6, 8, 59] and its statistical performance has been studied by Zhang [72] (see also [57, 30, 68, 53, 70] for similar bounds using empirical process theory)”
Nonparametric Instrumental Variable Estimation Under Monotonicity (2015, unknown): “A P] 1 9 Ju l 2 01”
On matrix estimation under monotonicity constraints (2015, background): “Zhang [29], among other things, showed the existence of a universal positive constant C such that”
Nonparametric Least Squares Estimation of a Multivariate Convex Regression Function (2010, background): “1633 recently, Zhang (2002) for literature concerning isotonic regression.”