Fetching the paper…
Reading the bibliography…
We consider the problem of estimating an unknown $\theta\in {\mathbb{R}}^n$ from noisy observations under the constraint that $\theta$ belongs to certain convex polyhedral cones in ${\mathbb{R}}^n$.
Ayer, MiriamM., Brunk, H. D.H. D., Ewing, G. M.G. M., Reid, W. T.W. T. andSilverman, EdwardE. (1955). An empirical distribution function for sampling with incomplete information. Ann. Math. Statist. 26 641–647
1955
Earlier work this paper cites.
Brunk, H. D.H. D. (1955). Maximum likelihood estimates of monotone parameters. Ann. Math. Statist. 26 607–616
1955
Earlier work this paper cites.
Grenander, UlfU. (1956). On the theory of mortality measurement. II. Skand. Aktuarietidskr. 39 125–153
1956
Earlier work this paper cites.
Brunk, H. D.H. D. (1970). Estimation of isotonic regression. In Nonparametric Techniques in Statistical Inference (Proc. Sympos., Indiana Univ., Bloomington, Ind., 1969) 177–197. Cambridge Univ. Press, London
1969
Earlier work this paper cites.
Wright, F. T.F. T. (1981). The asymptotic behavior of monotone regression estimates. Ann. Statist. 9 443–448
1981
Earlier work this paper cites.
Groeneboom, PietP. (1983). The concave majorant of Brownian motion. Ann. Probab. 11 1016–1027
1983
Earlier work this paper cites.
Groeneboom, P.P. (1985). Estimating a monotone density. In Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, Vol. II (Berkeley, Calif., 1983). 539–555. Wadsworth, Belmont, CA
1983
Earlier work this paper cites.
Schrijver, AlexanderA. (1986). Theory of Linear and Integer Programming. Wiley, Chichester
1986
Earlier work this paper cites.
Robertson, TimT., Wright, F. T.F. T. andDykstra, R. L.R. L. (1988). Order Restricted Statistical Inference. Wiley, Chichester
1988
Earlier work this paper cites.
Birgé, LucienL. (1989). The Grenander estimator: A nonasymptotic approach. Ann. Statist. 17 1532–1549
1989
Earlier work this paper cites.
van de Geer, SaraS. (1990). Estimating a regression function. Ann. Statist. 18 907–924
1990
Earlier work this paper cites.
Donoho, D.D. (1991). Gel’fand n n -widths and the method of least squares. Technical report, Dept. Statistics, Univ. California, Berkeley, CA
1991
Earlier work this paper cites.
Birgé, LucienL. andMassart, PascalP. (1993). Rates of convergence for minimum contrast estimators. Probab. Theory Related Fields 97 113–150
1993
Cited alongside, same era.
van de Geer, SaraS. (1993). Hellinger-consistency of certain nonparametric maximum likelihood estimators. Ann. Statist. 21 14–44
1993
Cited alongside, same era.
Wang, YazhenY. (1996). The L 2 L_{2} risk of an isotonic estimate. Comm. Statist. Theory Methods 25 281–294
1996
Cited alongside, same era.
van der Vaart, A. W.A. W. (1998). Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics 3. Cambridge Univ. Press, Cambridge
1998
Cited alongside, same era.
Barron, AndrewA., Birgé, LucienL. andMassart, PascalP. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113 301–413
1999
Cited alongside, same era.
Durrett, RickR. (2010). Probability: Theory and Examples, 4th ed. Cambridge Univ. Press, Cambridge
2010
Later among the works it cites.
Cai, T.T. andLow, M.M. (2011). A framework for estimation of convex functions. Available at http://www-stat.wharton.upenn.edu/~tcai/
2011
Later among the works it cites.
Cator, EricE. (2011). Adaptivity and optimality of the monotone least-squares estimator. Bernoulli 17 714–735
2011
Later among the works it cites.
Chandrasekaran, VenkatV., Recht, BenjaminB., Parrilo, Pablo A.P. A. andWillsky, Alan S.A. S. (2012). The convex geometry of linear inverse problems. Found. Comput. Math. 12 805–849
2012
Later among the works it cites.
Rigollet, PhilippeP. andTsybakov, Alexandre B.A. B. (2012). Sparse estimation by exponential weighting. Statist. Sci. 27 558–575
2012
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Carolan, ChrisC. andDykstra, RichardR. (1999). Asymptotic behavior of the Grenander estimator at density flat regions. Canad. J. Statist. 27 557–566
1999
Cited alongside, same era.
Meyer, MaryM. andWoodroofe, MichaelM. (2000). On the degrees of freedom in shape-restricted regression. Ann. Statist. 28 1083–1104
2000
Cited alongside, same era.
Zhang, Cun-HuiC.-H. (2002). Risk bounds in isotonic regression. Ann. Statist. 30 528–555
2002
Cited alongside, same era.
Bertsekas, Dimitri P.D. P. (2003). Convex Analysis and Optimization. Athena Scientific, Belmont, MA
2003
Cited alongside, same era.
Rudelson, MarkM. andVershynin, RomanR. (2006). Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements. In 40th Annual Conference on Information Sciences and Systems 207–212. IEEE, New York
2006
Cited alongside, same era.
2009
Cited alongside, same era.
Tsybakov, Alexandre B.A. B. (2009). Introduction to Nonparametric Estimation. Springer, New York
2009
Cited alongside, same era.
2013
Closest in time.
2013
Closest in time.
Guntuboyina, AdityanandA. andSen, BodhisattvaB. (2014). Global risk bounds and adaptation in univariate convex regression. Probab. Theory Related Fields
2014
Closest in time.
Jankowski, HannaH. (2014). Convergence of linear functionals of the Grenander estimator under misspecification. Ann. Statist. 42 625–653
2014
Closest in time.
Vershynin, RomanR. (2014). Lectures in geometric functional analysis. Available at \surl
2014
Closest in time.
Chatterjee, SabyasachiS., Guntuboyina, AdityanandA. andSen, BodhisattvaB. (2015). Supplement to “On risk bounds in isotonic and other shape restricted regression problems.” DOI: \doiurl
2015
Closest in time.