Edit Profile (opens in new tab) Low, Mark G. Compute Distance To: Compute Author ID: low.mark-g Published as: Low, Mark G.; Low, Mark Documents Indexed: 36 Publications since 1991 1 Contribution as Editor Co-Authors: 14 Co-Authors with 30 Joint Publications 505 Co-Co-Authors all top 5 Co-Authors 6 single-authored 17 Cai, Tony Tony 6 Brown, Lawrence David 3 Efromovich, Sam 3 Zhao, Linda H. 2 Ma, Zongming 2 Zhang, Cun-Hui 1 Carter, Andrew V. 1 Donoho, David Leigh 1 Jin, Jiashun 1 Kang, Yung-Gyung 1 Munk, Axel 1 Perktold, Karl 1 Rappitsch, Gerhard 1 Tsybakov, Alexandre B. 1 Xia, Yin 1 Zhou, Harrison H. all top 5 Serials 27 The Annals of Statistics 2 Bernoulli 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Journal of the American Statistical Association 1 Journal of Multivariate Analysis 1 Statistics & Probability Letters 1 Probability Theory and Related Fields 1 Journal of Nonparametric Statistics 1 Oberwolfach Reports all top 5 Fields 36 Statistics (62-XX) 3 Probability theory and stochastic processes (60-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Numerical analysis (65-XX) 1 General and overarching topics; collections (00-XX) 1 Fluid mechanics (76-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 34 Publications have been cited 759 times in 437 Documents Cited by ▼ Year ▼ Asymptotic equivalence of nonparametric regression and white noise. Zbl 0867.62022Brown, Lawrence D.; Low, Mark G. 163 1996 A constrained risk inequality with applications to nonparametric functional estimation. Zbl 0867.62023Brown, Lawrence D.; Low, Mark G. 54 1996 On nonparametric confidence intervals. Zbl 0894.62055Low, Mark G. 48 1997 Estimation and confidence sets for sparse normal mixtures. Zbl 1360.62113Cai, T. Tony; Jin, Jiashun; Low, Mark G. 42 2007 An adaptation theory for nonparametric confidence intervals. Zbl 1056.62060Cai, T. Tony; Low, Mark G. 39 2004 Renormalization exponents and optimal pointwise rates of convergence. Zbl 0797.62032Donoho, David L.; Low, Mark G. 38 1992 Adaptive confidence balls. Zbl 1091.62037Cai, T. Tony; Low, Mark G. 37 2006 Asymptotic equivalence theory for nonparametric regression with random design. Zbl 1029.62044Brown, Lawrence D.; Cai, T. Tony; Low, Mark G.; Zhang, Cun-Hui 33 2002 Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift. Zbl 1062.62083Brown, Lawrence D.; Carter, Andrew V.; Low, Mark G.; Zhang, Cun-Hui 30 2004 Nonquadratic estimators of a quadratic functional. Zbl 1085.62055Cai, T. Tony; Low, Mark G. 27 2005 Superefficiency in nonparametric function estimation. Zbl 0895.62043Brown, Lawrence D.; Low, Mark G.; Zhao, Linda H. 23 1997 On optimal adaptive estimation of a quadratic functional. Zbl 0865.62024Efromovich, Sam; Low, Mark 22 1996 Optimal adaptive estimation of a quadratic functional. Zbl 1110.62048Cai, T. Tony; Low, Mark G. 22 2006 Minimax estimation of linear functionals over nonconvex parameter spaces. Zbl 1048.62054Cai, T. Tony; Low, Mark G. 20 2004 Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional. Zbl 1277.62101Cai, T. Tony; Low, Mark G. 19 2011 Adaptive estimates of linear functionals. Zbl 0796.62037Efromovich, Sam; Low, Mark G. 18 1994 On adaptive estimation of linear functionals. Zbl 1086.62031Cai, T. Tony; Low, Mark G. 16 2005 Adaptive confidence bands for nonparametric regression functions. Zbl 1368.62093Cai, T. Tony; Low, Mark; Ma, Zongming 12 2014 A note on nonparametric estimation of linear functionals. Zbl 1105.62325Cai, T. Tony; Low, Mark G. 11 2003 Renormalization and white noise approximation for nonparametric functional estimation problems. Zbl 0756.62018Low, Mark G. 9 1992 Adaptive estimation of linear functionals under different performance measures. Zbl 1063.62045Cai, T. Tony; Low, Mark G. 8 2005 Adaptive confidence intervals for regression functions under shape constraints. Zbl 1267.62066Cai, T. Tony; Low, Mark G.; Xia, Yin 8 2013 Trade-offs between global and local risks in nonparametric function estimation. Zbl 1111.62029Cai, T. Tony; Low, Mark G.; Zhao, Linda H. 8 2007 On Bickel and Ritov’s conjecture about adaptive estimation of the integral of the square of density derivative. Zbl 0859.62039Efromovich, Sam; Low, Mark 7 1996 Sharp adaptive estimation by a blockwise method. Zbl 1172.62024Cai, T. Tony; Low, Mark G.; Zhao, Linda H. 7 2009 Bias-variance tradeoffs in functional estimation problems. Zbl 0838.62006Low, Mark G. 6 1995 Information inequality bounds on the minimax risk (with an application to nonparametric regression). Zbl 0736.62019Brown, Lawrence D.; Low, Mark G. 6 1991 Nonparametric estimation over shrinking neighborhoods: superefficiency and adaptation. Zbl 1064.62032Cai, T. Tony; Low, Mark G. 6 2005 A complement to Le Cam’s theorem. Zbl 1194.62007Low, Mark G.; Zhou, Harrison H. 6 2007 Non-existence of an adaptive estimator for the value of an unknown probability density. Zbl 0745.62035Low, Mark G. 4 1992 Estimating monotone functions. Zbl 1011.62036Low, Mark G.; Kang, Yung-Gyung 4 2002 Adaptation under probabilistic error for estimating linear functionals. Zbl 1078.62105Cai, T. Tony; Low, Mark G. 3 2006 Renormalizing upper and lower bounds for integrated risk in the white noise model. Zbl 0795.62038Low, Mark G. 2 1993 Discussion of “Frequentist coverage of adaptive nonparametric Bayesian credible sets”. Zbl 1321.62042Low, Mark G.; Ma, Zongming 1 2015 Discussion of “Frequentist coverage of adaptive nonparametric Bayesian credible sets”. Zbl 1321.62042Low, Mark G.; Ma, Zongming 1 2015 Adaptive confidence bands for nonparametric regression functions. Zbl 1368.62093Cai, T. Tony; Low, Mark; Ma, Zongming 12 2014 Adaptive confidence intervals for regression functions under shape constraints. Zbl 1267.62066Cai, T. Tony; Low, Mark G.; Xia, Yin 8 2013 Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional. Zbl 1277.62101Cai, T. Tony; Low, Mark G. 19 2011 Sharp adaptive estimation by a blockwise method. Zbl 1172.62024Cai, T. Tony; Low, Mark G.; Zhao, Linda H. 7 2009 Estimation and confidence sets for sparse normal mixtures. Zbl 1360.62113Cai, T. Tony; Jin, Jiashun; Low, Mark G. 42 2007 Trade-offs between global and local risks in nonparametric function estimation. Zbl 1111.62029Cai, T. Tony; Low, Mark G.; Zhao, Linda H. 8 2007 A complement to Le Cam’s theorem. Zbl 1194.62007Low, Mark G.; Zhou, Harrison H. 6 2007 Adaptive confidence balls. Zbl 1091.62037Cai, T. Tony; Low, Mark G. 37 2006 Optimal adaptive estimation of a quadratic functional. Zbl 1110.62048Cai, T. Tony; Low, Mark G. 22 2006 Adaptation under probabilistic error for estimating linear functionals. Zbl 1078.62105Cai, T. Tony; Low, Mark G. 3 2006 Nonquadratic estimators of a quadratic functional. Zbl 1085.62055Cai, T. Tony; Low, Mark G. 27 2005 On adaptive estimation of linear functionals. Zbl 1086.62031Cai, T. Tony; Low, Mark G. 16 2005 Adaptive estimation of linear functionals under different performance measures. Zbl 1063.62045Cai, T. Tony; Low, Mark G. 8 2005 Nonparametric estimation over shrinking neighborhoods: superefficiency and adaptation. Zbl 1064.62032Cai, T. Tony; Low, Mark G. 6 2005 An adaptation theory for nonparametric confidence intervals. Zbl 1056.62060Cai, T. Tony; Low, Mark G. 39 2004 Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift. Zbl 1062.62083Brown, Lawrence D.; Carter, Andrew V.; Low, Mark G.; Zhang, Cun-Hui 30 2004 Minimax estimation of linear functionals over nonconvex parameter spaces. Zbl 1048.62054Cai, T. Tony; Low, Mark G. 20 2004 A note on nonparametric estimation of linear functionals. Zbl 1105.62325Cai, T. Tony; Low, Mark G. 11 2003 Asymptotic equivalence theory for nonparametric regression with random design. Zbl 1029.62044Brown, Lawrence D.; Cai, T. Tony; Low, Mark G.; Zhang, Cun-Hui 33 2002 Estimating monotone functions. Zbl 1011.62036Low, Mark G.; Kang, Yung-Gyung 4 2002 On nonparametric confidence intervals. Zbl 0894.62055Low, Mark G. 48 1997 Superefficiency in nonparametric function estimation. Zbl 0895.62043Brown, Lawrence D.; Low, Mark G.; Zhao, Linda H. 23 1997 Asymptotic equivalence of nonparametric regression and white noise. Zbl 0867.62022Brown, Lawrence D.; Low, Mark G. 163 1996 A constrained risk inequality with applications to nonparametric functional estimation. Zbl 0867.62023Brown, Lawrence D.; Low, Mark G. 54 1996 On optimal adaptive estimation of a quadratic functional. Zbl 0865.62024Efromovich, Sam; Low, Mark 22 1996 On Bickel and Ritov’s conjecture about adaptive estimation of the integral of the square of density derivative. Zbl 0859.62039Efromovich, Sam; Low, Mark 7 1996 Bias-variance tradeoffs in functional estimation problems. Zbl 0838.62006Low, Mark G. 6 1995 Adaptive estimates of linear functionals. Zbl 0796.62037Efromovich, Sam; Low, Mark G. 18 1994 Renormalizing upper and lower bounds for integrated risk in the white noise model. Zbl 0795.62038Low, Mark G. 2 1993 Renormalization exponents and optimal pointwise rates of convergence. Zbl 0797.62032Donoho, David L.; Low, Mark G. 38 1992 Renormalization and white noise approximation for nonparametric functional estimation problems. Zbl 0756.62018Low, Mark G. 9 1992 Non-existence of an adaptive estimator for the value of an unknown probability density. Zbl 0745.62035Low, Mark G. 4 1992 Information inequality bounds on the minimax risk (with an application to nonparametric regression). Zbl 0736.62019Brown, Lawrence D.; Low, Mark G. 6 1991 all cited Publications top 5 cited Publications all top 5 Cited by 418 Authors 30 Cai, Tony Tony 25 Low, Mark G. 13 Brown, Lawrence David 13 Efromovich, Sam 12 Van der Vaart, Adrianus Willem 12 Zhou, Harrison H. 11 Tsybakov, Alexandre B. 10 Nickl, Richard 9 Carpentier, Alexandra 8 Belitser, Eduard 8 Dalalyan, Arnak S. 8 Ingster, Yuriĭ Izmaĭlovich 8 Jin, Jiashun 7 Butucea, Cristina 7 Collier, Olivier 7 Hoffmann, Marc 7 Juditsky, Anatoli B. 6 Carter, Andrew V. 6 Goldenshluger, Alexander 6 Hall, Peter Gavin 6 Lepskiĭ, Oleg Vital’evich 6 Pensky, Marianna 6 Reiß, Markus 6 Szabó, Botond 6 Verzelen, Nicolas 6 Zhang, Cun-Hui 5 Castillo, Ismaël 5 Donoho, David Leigh 5 Ermakov, Mikhaĭl Sergeevich 5 Fan, Jianqing 5 Ghosal, Subhashis 5 Kolchinskiĭ, Vladimir I’ich 5 Nemirovski, Arkadi S. 5 Nussbaum, Michael 5 Yang, Yuhong 5 Zhao, Linda H. 4 Blanchard, Gilles 4 Comminges, Laetitia 4 Gao, Chao 4 Klemelä, Jussi 4 Laurent, Béatrice 4 Mariucci, Ester 4 Marteau, Clément 4 Rousseau, Judith 4 Sapatinas, Theofanis 4 Schmidt-Hieber, Johannes 4 Spokoiny, Vladimir G. 4 Trabs, Mathias 3 Babenko, Alexandra 3 Bickel, Peter John 3 Bigot, Jéremie 3 Birgé, Lucien 3 Bull, Adam D. 3 Chesneau, Christophe 3 DasGupta, Anirban 3 Dette, Holger 3 Dümbgen, Lutz 3 Durastanti, Claudio 3 Gayraud, Ghislaine 3 Ghosh, Jayanta Kumar 3 Gugushvili, Shota 3 Jeng, X. Jessie 3 Kerkyacharian, Gérard 3 Kim, Arlene Kyoung Hee 3 Kroll, Martin H. 3 Lian, Heng 3 Maugis-Rabusseau, Cathy 3 Meister, Alexander 3 Mukherjee, Rajarshi 3 Neumann, Michael H. 3 Picard, Dominique B. 3 Ritov, Ya’acov 3 Rohde, Angelika 3 Roquain, Étienne 3 Sen, Bodhisattva 3 Suslina, Irina A. 3 van Zanten, J. H. 3 Wasserman, Larry Alan 3 Wishart, Justin Rory 3 Zeevi, Assaf J. 3 Zhilova, Mayya 2 Amato, Umberto 2 Angelini, Claudia 2 Armstrong, Timothy B. 2 Bandeira, Afonso S. 2 Baraud, Yannick 2 Belomestny, Denis 2 Benhaddou, Rida 2 Cai, Li 2 Candès, Emmanuel J. 2 Chakrabarti, Arijit 2 Chakraborty, Moumita 2 Chen, Jiahua 2 Chicken, Eric 2 De Canditiis, Daniela 2 Delattre, Sylvain 2 Enikeeva, Farida N. 2 Finner, Helmut 2 Gadat, Sébastien 2 Gaïffas, Stéphane ...and 318 more Authors all top 5 Cited in 68 Serials 148 The Annals of Statistics 33 Bernoulli 28 Electronic Journal of Statistics 18 Journal of Statistical Planning and Inference 16 Statistics & Probability Letters 15 Probability Theory and Related Fields 11 Journal of Multivariate Analysis 10 Annals of the Institute of Statistical Mathematics 9 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 9 Mathematical Methods of Statistics 9 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 8 Statistical Science 8 Journal of Nonparametric Statistics 6 Journal of the American Statistical Association 6 Sankhyā. Series A 5 Journal of Econometrics 5 Stochastic Processes and their Applications 5 SIAM/ASA Journal on Uncertainty Quantification 5 Mathematical Statistics and Learning 4 Scandinavian Journal of Statistics 4 Test 4 Statistical Inference for Stochastic Processes 4 Econometric Theory 3 Problems of Information Transmission 3 Applied and Computational Harmonic Analysis 3 Journal of the Royal Statistical Society. Series B. Statistical Methodology 2 Inverse Problems 2 Statistics 2 Sequential Analysis 2 Constructive Approximation 2 Computational Statistics 2 Communications in Statistics. Theory and Methods 2 Journal of Statistical Computation and Simulation 2 Statistical Papers 2 Statistica Sinica 2 Finance and Stochastics 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Journal of the European Mathematical Society (JEMS) 2 Journal of the Korean Statistical Society 2 The Annals of Applied Statistics 1 The Canadian Journal of Statistics 1 Biometrical Journal 1 Biometrics 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Results in Mathematics 1 Queueing Systems 1 Neural Networks 1 SIAM Journal on Applied Mathematics 1 Computational Statistics and Data Analysis 1 Mathematical Programming. Series A. Series B 1 Journal of Computer and Systems Sciences International 1 Journal of Mathematical Sciences (New York) 1 Australian & New Zealand Journal of Statistics 1 Chaos 1 Extremes 1 Communications of the Korean Mathematical Society 1 Statistical Methodology 1 AStA. Advances in Statistical Analysis 1 Probability Surveys 1 Statistics Surveys 1 Science China. Mathematics 1 Journal of Probability and Statistics 1 Symmetry 1 Information and Inference 1 Communications in Mathematics and Statistics 1 SIAM Journal on Mathematics of Data Science 1 Graduate Journal of Mathematics all top 5 Cited in 24 Fields 424 Statistics (62-XX) 57 Probability theory and stochastic processes (60-XX) 45 Numerical analysis (65-XX) 30 Harmonic analysis on Euclidean spaces (42-XX) 21 Information and communication theory, circuits (94-XX) 9 Functional analysis (46-XX) 6 Approximations and expansions (41-XX) 5 Partial differential equations (35-XX) 5 Computer science (68-XX) 5 Biology and other natural sciences (92-XX) 4 Quantum theory (81-XX) 4 Operations research, mathematical programming (90-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Systems theory; control (93-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) Citations by Year