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ANNALS OF STATISTICS, ISSN 0090-5364, 10/2019, Volume 47, Issue 5, pp. 2440 - 2471
We study the least squares regression function estimator over the class of real-valued functions on [0, 1](d) that are increasing in each coordinate. For... 
block increasing functions | sharp oracle inequality | RISK BOUNDS | ALGORITHM | CONCENTRATION INEQUALITIES | adaptation | STATISTICS & PROBABILITY | statistical dimension | LEAST-SQUARES | RATES | MODELS | Isotonic regression | least squares | CONVERGENCE | ENTROPY
Journal Article
Journal of Computer and System Sciences, ISSN 0022-0000, 02/2018, Volume 91, Issue C, pp. 69 - 81
Algorithms are given for determining weighted L∞ isotonic regressions satisfying order constraints given by a directed acyclic graph with n vertices and m... 
Isotonic regression | Tree | formula omitted | Dag | Monotonic | Linear order | Unimodal | Computer Science
Journal Article
Journal Article
ELECTRONIC JOURNAL OF STATISTICS, ISSN 1935-7524, 2019, Volume 13, Issue 1, pp. 710 - 746
This paper studies a two step procedure for monotone increasing additive single index models with Gaussian designs. The proposed procedure is simple, easy to... 
isotonic regression | OPTIMAL RATES | RISK BOUNDS | LASSO | STATISTICS & PROBABILITY | sparsity | Monotone single index models | high dimensional statistics | SELECTION | LEAST-SQUARES | INDEX MODELS
Journal Article
Technometrics, ISSN 0040-1706, 02/2011, Volume 53, Issue 1, pp. 54 - 61
Journal Article
Statistica Sinica, ISSN 1017-0405, 1/2018, Volume 28, Issue 1, pp. 277 - 292
The constrained partial linear model is fit using a single cone projection, without back-fitting. The cone formulation not only provides efficient computation,... 
Mathematical monotonicity | Voting | Linear regression | Spline functions | Inference | Mathematical vectors | Voter registration | Linear models | Estimators | Knots | Hypothesis testing | Constrained estimation | Isotonic | Smoothing | Convergence rates | isotonic | hypothesis testing | STATISTICS & PROBABILITY | convergence rates | smoothing | CONVERGENCE-RATES
Journal Article
Journal of Computational and Graphical Statistics, ISSN 1061-8600, 01/2014, Volume 23, Issue 1, pp. 192 - 210
We present a new computational and statistical approach for fitting isotonic models under convex differentiable loss functions through recursive partitioning.... 
Convex optimization | Regularization path | Nonparametric regression | Datasets | Integers | Outliers | Isotonic solutions | Algorithms | Optimal solutions | Iterative solutions | Regression analysis | Simulation training | Isotonicity | Regression Methods | ALGORITHM | CHAIN CONSTRAINTS | STATISTICS & PROBABILITY | RULE | CONVEX-FUNCTIONS SUBJECT
Journal Article
Algorithmica, ISSN 0178-4617, 5/2013, Volume 66, Issue 1, pp. 93 - 112
Journal Article
Bernoulli, ISSN 1350-7265, 02/2019, Volume 25, Issue 1, pp. 1 - 25
We study the statistical properties of the least squares estimator in unimodal sequence estimation. Although closely related to isotonic regression, unimodal... 
Unimodal regression | Minimax bounds | Isotonic regression | Shape constrained inference | isotonic regression | STATISTICS & PROBABILITY | unimodal regression | minimax bounds | LEAST-SQUARES | shape constrained inference
Journal Article
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 08/2019, Volume 41, Issue 8, pp. 1813 - 1827
In many real-world classification problems, accurate prediction of membership probabilities is critical for further decision making. The probability... 
Support vector machines | semidefinite programming | isotonic regression | Symmetric matrices | Computational modeling | Estimation | Training data | probability prediction | Calibration | Classification calibration | polynomial regression | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 04/2016, Volume 494, pp. 80 - 89
The note describes the cones in the Euclidean space admitting isotonic metric projection with respect to the coordinate-wise ordering. As a consequence it is... 
Quadratic optimization | Isotonic regression | Ordered Euclidean space | Isotonic projection | MATHEMATICS | MATHEMATICS, APPLIED | MONOTONICITY | SUBLATTICES | Computer science | Methamphetamine
Journal Article
Electronic Journal of Statistics, ISSN 1935-7524, 2017, Volume 11, Issue 2, pp. 4488 - 4514
Isotonic regression offers a flexible modeling approach under monotonicity assumptions, which are natural in many applications. Despite this attractive setting... 
Multivariate isotonic regression | Lasso regularization | Range regularization | Regularization path | Nonparametric regression | nonparametric regression | regularization path | lasso regularization | LASSO | SPLINES | FREEDOM | STATISTICS & PROBABILITY | RULE | range regularization
Journal Article
Biometrika, ISSN 0006-3444, 6/2014, Volume 101, Issue 2, pp. 303 - 317
Journal Article
Journal of Biopharmaceutical Statistics, ISSN 1054-3406, 09/2017, Volume 27, Issue 5, pp. 824 - 833
Understanding dose-response relationship is a crucial step in drug development. There are a few parametric methods to estimate dose-response curves, such as... 
isotonic regression | monotone function estimation | Bayesian method | dose response | PHARMACOLOGY & PHARMACY | STATISTICS & PROBABILITY
Journal Article
Journal of the American Statistical Association, ISSN 0162-1459, 01/2020, Volume 115, Issue 529, pp. 173 - 186
Abstract-In this article, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of... 
Multivariate convex regression | Bounded isotonic regression | Divergence of an estimator | Additive model | Generalized Lasso
Journal Article
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