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A Chernoff-type distribution is a nonnormal distribution defined by the slope at zero of the greatest convex minorant of a two-sided Brownian motion with a polynomial drift.
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by same author, Lectures on inverse problems , Lectures on probability theory and statistics (Saint-Flour, 1994), Lecture Notes in Math., vol. 1648, Springer, Berlin, 1996, pp. 67–164
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1996
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1996
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V. Bentkus, F. Götze, and A. Tikhomirov, Berry-Esseen bounds for statistics of weakly dependent samples , Bernoulli 3
1997
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by same author, On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted U U -statistics , Ann. Appl. Probab. 7
1997
by same author, A local maximal inequality under uniform entropy , Electron. J. Stat. 5
2011
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by same author, A new approach to strong embeddings , Probab. Theory Related Fields 152
2012
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Cécile Durot, Vladimir N. Kulikov, and Hendrik P. Lopuhaä, The limit distribution of the L ∞ L_{\infty} -error of Grenander-type estimators , Ann. Statist. 40
2012
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Dan Lin, Ziv Shkedy, Daniel Yekutieli, Dhammika Amaratunga, and Luc Bijnens, Modeling dose-response microarray data in early drug development experiments using r: order-restricted analysis of microarray data , Springer Science & Business Media, 2012
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Michael J Schell and Bahadur Singh, The reduced monotonic regression method , Journal of the American Statistical Association 92
1997
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Yu. A. Davydov, M. A. Lifschits, and N. V. Smorodina, Local properties of distributions of stochastic functionals , American Mathematical Society, 1998
1998
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Bert van Es, Geurt Jongbloed, and Martien van Zuijlen, Isotonic inverse estimators for nonparametric deconvolution , Ann. Statist. 26
1998
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Víctor H. de la Peña and Evarist Giné, Decoupling , Probability and its Applications (New York), Springer-Verlag, New York, 1999, From dependence to independence, Randomly stopped processes. U U -statistics and processes. Martingales and beyond
1999
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Piet Groeneboom, Gerard Hooghiemstra, and Hendrik P. Lopuhaä, Asymptotic normality of the L 1 L_{1} error of the Grenander estimator , Ann. Statist. 27
1999
Cited alongside, same era.
2000
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by same author, Computing Chernoff’s distribution , J. Comput. Graph. Statist. 10
2001
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2012
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Victor Chernozhukov, Denis Chetverikov, and Kengo Kato, Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors , Ann. Statist. 41
2013
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Fadoua Balabdaoui and Jon A. Wellner, Chernoff’s density is log-concave , Bernoulli 20
2014
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by same author, Gaussian approximation of suprema of empirical processes , Ann. Statist. 42
2014
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Piet Groeneboom and Geurt Jongbloed, Nonparametric estimation under shape constraints , Cambridge Series in Statistical and Probabilistic Mathematics, vol. 38, Cambridge University Press, New York, 2014
2014
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Hanna Jankowski, Convergence of linear functionals of the Grenander estimator under misspecification , Ann. Statist. 42
2014
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2015
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Piet Groeneboom, Steven Lalley, and Nico Temme, Chernoff’s distribution and differential equations of parabolic and Airy type , J. Math. Anal. Appl. 423
2015
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2016
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Lutz Dümbgen, Jon A. Wellner, and Malcolm Wolff, A law of the iterated logarithm for Grenander’s estimator , Stochastic Process. Appl. 126
2016
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Evarist Giné and Richard Nickl, Mathematical foundations of infinite-dimensional statistical models , Cambridge Series in Statistical and Probabilistic Mathematics, [40], Cambridge University Press, New York, 2016
2016
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by same author, Central limit theorems and bootstrap in high dimensions , Ann. Probab. 45
2017
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by same author, Detailed proof of Nazarov’s inequality , arXiv preprint arXiv:1711.10696 (2017)
2017
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2017
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Richard J. Samworth and Bodhisattva Sen, Editorial: special issue on “Nonparametric inference under shape constraints” , Statist. Sci. 33
2018
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