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Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i, y_i)$ where $\mathbb{E}[y_i]=f(x_i), i=1, \ldots n$.
J. J. Deely and R. L. Kruse, Construction of sequences estimating the mixing distribution , Ann. Math. Statist. 39
1968
Earlier work this paper cites.
Jason Altschuler, Jonathan Weed, and Philippe Rigollet, Near-linear time approximation algorithms for optimal transport via sinkhorn iteration , Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, 4-9 December 2017, Long Beach, CA, USA, 2017, pp. 1961–1971
1971
Earlier work this paper cites.
R. E. Barlow, D. J. Bartholomew, J. M. Bremner, and H. D. Brunk, Statistical inference under order restrictions. The theory and application of isotonic regression , John Wiley & Sons, London-New York-Sydney, 1972, Wiley Series in Probability and Mathematical Statistics. MR0326887
1972
Earlier work this paper cites.
Morris H. DeGroot and Prem K. Goel, Estimation of the correlation coefficient from a broken random sample , Ann. Statist. 8
1980
Earlier work this paper cites.
A. S. Nemirovskiĭ, B. T. Polyak, and A. B. Tsybakov, The rate of convergence of nonparametric estimates of maximum likelihood type , Problemy Peredachi Informatsii 21
1985
Earlier work this paper cites.
Tim Robertson, F. T. Wright, and R. L. Dykstra, Order restricted statistical inference , Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Ltd., Chichester, 1988. MR961262
1988
Earlier work this paper cites.
Sara van de Geer, Estimating a regression function , Ann. Statist. 18
1990
Earlier work this paper cites.
Enno Mammen, Estimating a smooth monotone regression function , Ann. Statist. 19
1991
Earlier work this paper cites.
Jiahua Chen, Optimal rate of convergence for finite mixture models , The Annals of Statistics (1995), 221–233
1995
Earlier work this paper cites.
O. Lepski, A. Nemirovski, and V. Spokoiny, On estimation of the L r L_{r} norm of a regression function , Probab. Theory Related Fields 113
1999
Earlier work this paper cites.
Mary Meyer and Michael Woodroofe, On the degrees of freedom in shape-restricted regression , Ann. Statist. 28
2000
Earlier work this paper cites.
Anatoli Juditsky and Arkadi Nemirovski, On nonparametric tests of positivity/monotonicity/convexity , Ann. Statist. 30
2002
Earlier work this paper cites.
Cun-Hui Zhang, Risk bounds in isotonic regression , Ann. Statist. 30
2002
Earlier work this paper cites.
Cédric Villani, Topics in optimal transportation , Graduate Studies in Mathematics, vol. 58, American Mathematical Society, Providence, RI, 2003. MR1964483 (2004e:90003)
2003
Earlier work this paper cites.
Alexandre B. Tsybakov, Introduction to nonparametric estimation , Springer Series in Statistics, Springer, New York, 2009, Revised and extended from the 2004 French original, Translated by Vladimir Zaiats. MR2724359 (2011g:62006)
2004
Earlier work this paper cites.
Federico Bassetti, Antonella Bodini, and Eugenio Regazzini, On minimum kantorovich distance estimators , Statistics & Probability Letters 76
2006
Earlier work this paper cites.
Cédric Villani, Optimal transport: old and new , vol. 338, Springer Science & Business Media, 2008
2008
Earlier work this paper cites.
Philippe Flajolet and Robert Sedgewick, Analytic combinatorics , Cambridge University Press, Cambridge, 2009. MR2483235
2009
Cited alongside, same era.
Ankur Moitra and Gregory Valiant, Settling the polynomial learnability of mixtures of gaussians , Foundations of Computer Science (FOCS), 2010 51st Annual IEEE Symposium on, IEEE, 2010, pp. 93–102
2010
Cited alongside, same era.
Claire Caillerie, Frédéric Chazal, Jérôme Dedecker, and Bertrand Michel, Deconvolution for the Wasserstein metric and geometric inference , Electron. J. Stat. 5
2011
Cited alongside, same era.
T Tony Cai and Mark G. Low, Testing composite hypotheses, hermite polynomials and optimal estimation of a nonsmooth functional , The Annals of Statistics 39
2011
Cited alongside, same era.
I. Dattner, A. Goldenshluger, and A. Juditsky, On deconvolution of distribution functions , Ann. Statist. 39
2017
Later among the works it cites.
A. Carpentier and N. Verzelen, Adaptive estimation of the sparsity in the Gaussian vector model , ArXiv: 1703.00167 (2017)
2017
Later among the works it cites.
Daniel J. Hsu, Kevin Shi, and Xiaorui Sun, Linear regression without correspondence , Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, 4-9 December 2017, Long Beach, CA, USA (Isabelle Guyon, Ulrike von Luxburg, Samy Bengio, Hanna M. Wallach, Rob Fergus, S. V. N. Vishwanathan, and Roman Garnett, eds.), 2017, pp. 1530–1539
2017
Later among the works it cites.
2017
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2011
Cited alongside, same era.
Marco Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport , Advances in Neural Information Processing Systems 26 (C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Q. Weinberger, eds.), Curran Associates, Inc., 2013, pp. 2292–2300
2013
Cited alongside, same era.
Jérôme Dedecker and Bertrand Michel, Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension , J. Multivariate Anal. 122
2013
Cited alongside, same era.
Georg Ch. Pflug and Alois Pichler, Multistage stochastic optimization , Springer Series in Operations Research and Financial Engineering, Springer, Cham, 2014. MR3288310
2014
Cited alongside, same era.
Pierre C. Bellec and Alexandre B. Tsybakov, Sharp oracle bounds for monotone and convex regression through aggregation , J. Mach. Learn. Res. 16
2015
Cited alongside, same era.
Jérôme Dedecker, Aurélie Fischer, and Bertrand Michel, Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one , Electron. J. Stat. 9
2015
Cited alongside, same era.
2015
Cited alongside, same era.
Filippo Santambrogio, Optimal transport for applied mathematicians , Birkäuser, NY (2015)
2015
Cited alongside, same era.
Later among the works it cites.
Weihao Kong and Gregory Valiant, Spectrum estimation from samples , Ann. Statist. 45
2017
Later among the works it cites.
Ashwin Pananjady, Martin J. Wainwright, and Thomas A. Courtade, Denoising linear models with permuted data , 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, June 25-30, 2017, IEEE, 2017, pp. 446–450
2017
Later among the works it cites.
2017
Later among the works it cites.
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