Fetching the paper…
Reading the bibliography…
We study the adaptation properties of the multivariate log-concave maximum likelihood estimator over three subclasses of log-concave densities.
Available at https://arxiv.org/abs/1903.05315
Kur, G., Dagan, Y. and Rakhlin, A. (2019). Optimality of maximum likelihood for log-concave density estimation and bounded convex regression · 1903
Earlier work this paper cites.
Available at https://arxiv.org/abs/1903.06092
Xu, M. and Samworth, R. J. (2019). High-dimensional nonparametric density estimation via symmetry and shape constraints · 1903
Earlier work this paper cites.
Available at https://arxiv.org/abs/1905.12823v1
Han, Q. (2019). Global empirical risk minimizers with “shape constraints” are rate optimal in general dimensions · 1905
Earlier work this paper cites.
In Studies and essays presented to R. Courant on his 60th birthday
John, F. (1948). Extremum problems with inequalities as subsidiary conditions · 1948
Earlier work this paper cites.
IEEE Trans. Inf. Th. , 59
Guntuboyina, A. and Sen, B. (2013). Covering numbers for convex functions · 1965
Earlier work this paper cites.
Siberian Math. J
Bronshteyn, E. M. and Ivanov, L. (1975). The approximation of convex sets by polyhedra · 1975
Earlier work this paper cites.
Combinatorica , 5
Rothschild, B. L. and Straus, E. G. (1985). On triangulations of the convex hull of n n points · 1985
Earlier work this paper cites.
Arch. Math
Lang, R. (1986). A note on the measurability of convex sets · 1986
Earlier work this paper cites.
Ann. Statist. , 15
Birgé, L. (1987). Estimating a density under order restrictions: nonasymptotic minimax risk · 1987
Earlier work this paper cites.
Wieacker, J. A. (1987). Einige Probleme der polyedrischen Approximation . Diplomarbeit, Freiburg
1987
Earlier work this paper cites.
J. Symbolic Comput. , 10
Edelsbrunner, H., Preparata, F. P. and West, D. B. (1990). Tetrahedrizing point sets in three dimensions · 1990
Earlier work this paper cites.
Geometriae Dedicata
Gordon, Y., Meyer, M. and Reisner, S. (1995). Constructing a polytope to approximate a convex body · 1995
Earlier work this paper cites.
Ann. Probab. , 24
Bobkov, S. G. (1996). Extremal properties of half-spaces for log-concave distributions · 1996
Earlier work this paper cites.
Princeton University Press, Princeton
Rockafellar, R. T. (1997). Convex Analysis · 1997
Earlier work this paper cites.
Cambridge University Press, Cambridge
van der Vaart, A. W. (1998). Asymptotic Statistics · 1998
Earlier work this paper cites.
Cambridge University Press, Cambridge
van de Geer, S. A. (2000). Empirical Processes in M-Estimation · 2000
Earlier work this paper cites.
In Lecture Notes in Computer Science
Wang, C. A. and Yang, B. (2000). Tetrahedralization of two nested convex polyhedra · 2000
Earlier work this paper cites.
Zhang, C.-H. (2002). Risk bounds in isotonic regression. Ann. Statist. , 30
2002
Earlier work this paper cites.
In Handbook of Discrete and Computational Geometry
Henk, M., Richter-Gebert, J. and Ziegler, G. M. (2004). Basic properties of convex polytopes · 2004
Earlier work this paper cites.
In Handbook of Discrete and Computational Geometry
Kalai, G. (2004). Polytope skeletons and paths · 2004
Earlier work this paper cites.
In Handbook of Discrete and Computational Geometry
Lee, C. W. (2004). Subdivisions and triangulations of polytopes · 2004
Earlier work this paper cites.
Ann. Statist. , 34
Gardner, R. J., Kiderlen, M. and Milanfar, P. (2006). Convergence of algorithms for reconstructing convex bodies and directional measures · 2006
Earlier work this paper cites.
Random Struct. Alg. , 30
Lovász, L. and Vempala, S. (2006). The geometry of logconcave functions and sampling algorithms · 2006
Earlier work this paper cites.
Ann. Statist. , 37
Balabdaoui F., Rufibach K. and Wellner, J. A. (2009). Limit distribution theory for pointwise maximum likelihood estimation of a log-concave density · 2009
Cited alongside, same era.
Springer–Verlag, New York
Bruns, W. and Gubeladze, J. (2009). Polytopes, Rings and K-theory · 2009
Cited alongside, same era.
Bernoulli , 15
Dümbgen, L. and Rufibach, K. (2009). Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency · 2009
Cited alongside, same era.
Stat. Sci. , 24
Walther, G. (2009). Inference and modeling with log-concave densities · 2009
Cited alongside, same era.
Electron. J. Stat. , 4
Cule, M. and Samworth, R. (2010). Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density · 2010
Cited alongside, same era.
Cule, M., Samworth, R. and Stewart, M. (2010). Maximum likelihood estimation of a multi-dimensional log-concave density. J. Roy. Statist. Soc., Ser. B. (with discussion)
Ann. Statist. , 43
Chatterjee, S., Guntuboyina, A. and Sen, B. (2015). On risk bounds in isotonic and other shape restricted regression problems · 2015
Later among the works it cites.
Stoch. Proc. Appl. , 12
Baraud, Y. and Birgé, L. (2016). Rates of convergence of rho-estimators for sets of densities satisfying shape constraints · 2016
Later among the works it cites.
J. Roy. Statist. Soc., Ser. B , 78
Chen, Y. and Samworth, R. J. (2016). Generalised additive and index models with shape constraints · 2016
Later among the works it cites.
Ann. Statist. , 44
Doss, C. R. and Wellner, J. A. (2016). Global rates of convergence of the MLEs of log-concave and s s -concave densities · 2016
Later among the works it cites.
Available at https://arxiv.org/abs/1601.06844
Han, Q. and Wellner, J. A. (2016). Multivariate convex regression: global risk bounds and adaptation · 2016
Later among the works it cites.
Ann. Statist. , 44
Kim, A. K. H. and Samworth, R. J. (2016). Global rates of convergence in log-concave density estimation · 2016
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2010
Cited alongside, same era.
Ann. Statist. , 38
Seregin, A. and Wellner, J. A. (2010). Nonparametric estimation of multivariate convex-transformed densities · 2010
Cited alongside, same era.
Ann. Statist. , 39
Dümbgen, L., Samworth, R. and Schuhmacher, D. (2011). Approximation by log-concave distributions, with applications to regression · 2011
Cited alongside, same era.
Geom. Func. Anal. , 21
Guédon, O. and Milman, E. (2011). Interpolating thin-shell and sharp large-deviation estimates for isotropic log-concave measures · 2011
Cited alongside, same era.
Ann. Statist. , 40
Guntuboyina, A. (2012). Optimal rates of convergence for convex set estimation from support functions · 2012
Cited alongside, same era.
Ann. Statist. , 40
Samworth, R. J. and Yuan, M. (2012). Independent component analysis via nonparametric maximum likelihood estimation · 2012
Cited alongside, same era.
Electron. J. Statist. , 7
Brunel, V.-E. (2013). Adaptive estimation of convex polytopes and convex sets from noisy data · 2013
Cited alongside, same era.
Later among the works it cites.
Ann. Statist. , 44
Xu, M., Chen, M. and Lafferty, J. (2016). Faithful variable screening for high-dimensional convex regression · 2016
Later among the works it cites.
Constr. Approx
Gao, F. and Wellner, J. A. (2017). Entropy of convex functions on ℝ d \mathbb{R}^{d} · 2017
Later among the works it cites.
IEEE Trans. Inf. Th. , 63
Shah, N., Balakrishnan, S., Guntuboyina, A. and Wainwright, M. J. (2017). Stochastically transitive models for pairwise comparisons: Statistical and computational issues · 2017
Later among the works it cites.
Bellec, P. C. (2018). Sharp oracle inequalities for least squares estimators in shape restricted regression. Ann. Statist. , 46
2018
Closest in time.
Proc. Mach. Learn. Res. , 75
Carpenter, T., Diakonikolas, I., Sidiropoulos, A. and Stewart A. (2018). Near-optimal sample complexity bounds for maximum likelihood estimation of multivariate log-concave densities · 2018
Closest in time.
Bernoulli , 24
Chatterjee, S., Guntuboyina, A. and Sen, B. (2018). On matrix estimation under monotonicity constraints · 2018
Closest in time.
Available at https://arxiv.org/abs/1812.08944
Deng, H. and Zhang, C.-H. (2018). Isotonic regression in multi-dimensional spaces and graphs · 2018
Closest in time.
Ann. Statist. , 46
Groeneboom, P. and Hendrickx, K. (2018). Current status linear regression · 2018
Closest in time.
Ann. Statist. , 46
Kim, A. K. H., Guntuboyina, A. and Samworth, R. J. (2018). Adaptation in log-concave density estimation · 2018
Closest in time.
J. Amer. Statist. Assoc. , 114
Mazumder, R., Choudhury, A., Iyengar, G. and Sen, B. (2018). A computational framework for multivariate convex regression and its variants · 2018
Closest in time.
Stat. Sci. , 33
Samworth, R. J. (2018). Recent progress in log-concave density estimation · 2018
Closest in time.
Bernoulli , 25
Chatterjee, S. and Lafferty, J. (2019). Adaptive risk bounds in unimodal regression · 2019
Closest in time.
Submitted
Feng, O. Y., Guntuboyina, A., Kim, A. K. H. and Samworth, R. J. (2019). Adaptation in multivariate log-concave density estimation · 2019
Closest in time.
Submitted
Feng, O. Y., Guntuboyina, A., Kim, A. K. H. and Samworth, R. J. (2019). Supplementary material for ‘Adaptation in multivariate log-concave density estimation’ · 2019
Closest in time.
Ann. Statist. , 47
Han, Q., Wang, T., Chatterjee, S. and Samworth, R. J. (2019). Isotonic regression in general dimensions · 2019
Closest in time.
Electron. J. Statist. , 13
Soloff, J. A., Guntuboyina, A. and Pitman, J. (2019). Distribution-free properties of isotonic regression · 2019
Closest in time.