×

Editorial: Special issue on “Nonparametric inference under shape constraints”. (English) Zbl 1407.00039

From the text: This unprecedented growth has signalled the need for a special issue on shape-constrained statistical methods and, as Guest Editors, we hope that it will serve as a gateway to this exciting field of research. We have eight articles, as well as one conversation piece, written by experts in their respective sub-fields that showcase the main shape-constrained models of interest, a variety of applications of such models, and the major recent theoretical, methodological and computational advances in some of these problems.

MSC:

00B15 Collections of articles of miscellaneous specific interest
62-06 Proceedings, conferences, collections, etc. pertaining to statistics
62G05 Nonparametric estimation

Software:

cgam; scar; LogConcDEAD

References:

[1] Balabdaoui, F., Rufibach, K. and Wellner, J. A. (2009). Limit distribution theory for maximum likelihood estimation of a log-concave density. Ann. Statist.37 1299-1331. · Zbl 1160.62008 · doi:10.1214/08-AOS609
[2] Banerjee, M. and Samworth, R. J. (2018). A conversation with Jon Wellner. Statist. Sci.33 633-651. · Zbl 1407.01015
[3] Banerjee, M. and Wellner, J. A. (2001). Likelihood ratio tests for monotone functions. Ann. Statist.29 1699-1731. · Zbl 1043.62037 · doi:10.1214/aos/1015345959
[4] Barlow, R. E., Bartholomew, D. J., Bremner, J. M. and Brunk, H. D. (1972). Statistical Inference Under Order Restrictions. The Theory and Application of Isotonic Regression. Wiley, London. · Zbl 0246.62038
[5] Birgé, L. (1989). The Grenander estimator: A nonasymptotic approach. Ann. Statist.17 1532-1549. · Zbl 0703.62042 · doi:10.1214/aos/1176347380
[6] Brunel, V.-E. (2013). Adaptive estimation of convex polytopes and convex sets from noisy data. Electron. J. Stat.7 1301-1327. · Zbl 1336.62127 · doi:10.1214/13-EJS804
[7] Brunel, V.-E. (2018). Methods for estimation of convex sets. Statist. Sci.33 615-632. · Zbl 1407.62115
[8] Cai, T. T. and Low, M. G. (2015). A framework for estimation of convex functions. Statist. Sinica25 423-456. · Zbl 1534.62033
[9] Chen, Y. and Samworth, R. J. (2016). Generalized additive and index models with shape constraints. J. R. Stat. Soc. Ser. B. Stat. Methodol.78 729-754. · Zbl 1414.62153
[10] Cule, M., Samworth, R. and Stewart, M. (2010). Maximum likelihood estimation of a multi-dimensional log-concave density. J. R. Stat. Soc. Ser. B. Stat. Methodol.72 545-607. · Zbl 1329.62183 · doi:10.1214/09-EJS505
[11] Dümbgen, L. and Rufibach, K. (2009). Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency. Bernoulli15 40-68. · Zbl 1200.62030 · doi:10.3150/08-BEJ141
[12] Dümbgen, L., Samworth, R. and Schuhmacher, D. (2011). Approximation by log-concave distributions, with applications to regression. Ann. Statist.39 702-730. · Zbl 1216.62023 · doi:10.1214/10-AOS853
[13] Durot, C. and Lopuhaä, H. (2018). Limit theory in monotone function estimation. Statist. Sci.33 547-567. · Zbl 1407.62105
[14] Gardner, R. J. (2006). Geometric Tomography, 2nd ed. Encyclopedia of Mathematics and Its Applications58. Cambridge Univ. Press, New York. · Zbl 1102.52002
[15] Gardner, R. J., Kiderlen, M. and Milanfar, P. (2006). Convergence of algorithms for reconstructing convex bodies and directional measures. Ann. Statist.34 1331-1374. · Zbl 1097.52503 · doi:10.1214/009053606000000335
[16] Grenander, U. (1956). On the theory of mortality measurement. II. Skand. Aktuarietidskr.39 125-153. · Zbl 0077.33715
[17] Groeneboom, 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. · Zbl 1373.62144
[18] Groeneboom, P. and Hendrickx, K. (2018). Current status linear regression. Ann. Statist.46 1415-1444. · Zbl 1403.62046 · doi:10.1214/17-AOS1589
[19] Groeneboom, P. and Jongbloed, G. (2014). Nonparametric Estimation Under Shape Constraints: Estimators, Algorithms and Asymptotics. Cambridge Series in Statistical and Probabilistic Mathematics38. Cambridge Univ. Press, New York. · Zbl 1338.62008
[20] Groeneboom, P. and Jongbloed, G. (2018). Some developments in the theory of shape constrained inference. Statist. Sci.33 473-492. · Zbl 1407.62108
[21] Groeneboom, P., Jongbloed, G. and Wellner, J. A. (2001). Estimation of a convex function: Characterizations and asymptotic theory. Ann. Statist.29 1653-1698. · Zbl 1043.62027 · doi:10.1214/aos/1015345958
[22] Groeneboom, P. and Wellner, J. A. (1992). Information Bounds and Nonparametric Maximum Likelihood Estimation. DMV Seminar19. Birkhäuser, Basel. · Zbl 0757.62017
[23] Guntuboyina, A. (2012). Optimal rates of convergence for convex set estimation from support functions. Ann. Statist.40 385-411. · Zbl 1246.62085 · doi:10.1214/11-AOS959
[24] Guntuboyina, A. and Sen, B. (2013). Covering numbers for convex functions. IEEE Trans. Inform. Theory59 1957-1965. · Zbl 1364.52007 · doi:10.1109/TIT.2012.2235172
[25] Guntuboyina, A. and Sen, B. (2018). Nonparametric shape-restricted regression. Statist. Sci.33 568-594. · Zbl 1407.62135
[26] Han, Q., Wang, T., Chatterjee, S. and Samworth, R. J. (2018). Isotonic regression in general dimensions. Ann. Statist. To appear. · Zbl 1437.62124
[27] Johnson, A. and Jiang, D. (2018). Shape constraints in economics and operations research. Statist. Sci.33 527-546. · Zbl 1407.62424
[28] Kim, A. K. H. and Samworth, R. J. (2016). Global rates of convergence in log-concave density estimation. Ann. Statist.44 2756-2779. · Zbl 1360.62157 · doi:10.1214/16-AOS1480
[29] Koenker, R. and Mizera, I. (2010). Quasi-concave density estimation. Ann. Statist.38 2998-3027. · Zbl 1200.62031 · doi:10.1214/10-AOS814
[30] Koenker, R. and Mizera, I. (2014). Convex optimization, shape constraints, compound decisions, and empirical Bayes rules. J. Amer. Statist. Assoc.109 674-685. · Zbl 1367.62020 · doi:10.1080/01621459.2013.869224
[31] Koenker, R. and Mizera, I. (2018). Shape constrained density estimation via penalized Rényi divergence. Statist. Sci.33 510-526. · Zbl 1407.62121
[32] Lin, D., Shkedy, Z., Yekutieli, D., Amaratunga, D. and Bijnens, L. (2012). Modeling Dose-Response Microarray Data in Early Drug Development Experiments Using R: Order-Restricted Analysis of Microarray Data. Springer, Heidelberg.
[33] Luss, R., Rosset, S. and Shahar, M. (2012). Efficient regularized isotonic regression with application to gene-gene interaction search. Ann. Appl. Stat.6 253-283. · Zbl 1235.62046 · doi:10.1214/11-AOAS504
[34] Matzkin, R. L. (1991). Semiparametric estimation of monotone and concave utility functions for polychotomous choice models. Econometrica59 1315-1327. · Zbl 0781.90009 · doi:10.2307/2938369
[35] Mazumder, R., Choudhury, A., Iyengar, G. and Sen, B. (2018). A computational framework for multivariate convex regression and its variants. J. Amer. Statist. Assoc. To appear. · Zbl 1418.62122
[36] Meyer, M. C. (2018). A framework for estimation and inference in generalized additive models with shape and order restrictions. Statist. Sci.33 595-614. · Zbl 1407.62278
[37] Prakasa Rao, B. L. S. (1969). Estimation of a unimodal density. Sankhyā Ser. A31 23-36. · Zbl 0181.45901
[38] Robertson, T., Wright, F. T. and Dykstra, R. L. (1988). Order Restricted Statistical Inference. Wiley, Chichester. · Zbl 0645.62028
[39] Samworth, R. J. (2018). Recent progress in log-concave density estimation. Statist. Sci.33 493-509. · Zbl 1407.62126
[40] Schell, M. J. and Singh, B. (1997). The reduced monotonic regression method. J. Amer. Statist. Assoc.92 128-135. · Zbl 0890.62035 · doi:10.1080/01621459.1997.10473609
[41] Seijo, E. and Sen, B. (2011). Nonparametric least squares estimation of a multivariate convex regression function. Ann. Statist.39 1633-1657. · Zbl 1220.62044 · doi:10.1214/10-AOS852
[42] Seregin, A. and Wellner, J. A. (2010). Nonparametric estimation of multivariate convex-transformed densities. Ann. Statist.38 3751-3781. · Zbl 1204.62058 · doi:10.1214/10-AOS840
[43] Shah, N. B., Balakrishnan, S., Guntuboyina, A. and Wainwright, M. J. (2017). Stochastically transitive models for pairwise comparisons: Statistical and computational issues. IEEE Trans. Inform. Theory63 934-959. · Zbl 1364.94253 · doi:10.1109/TIT.2016.2634418
[44] Varian, H. R. (1984). The nonparametric approach to production analysis. Econometrica52 579-597. · Zbl 0558.90024 · doi:10.2307/1913466
[45] Xu, M., Chen, M. and Lafferty, J. (2016). Faithful variable screening for high-dimensional convex regression. Ann. Statist.44 2624-2660. · Zbl 1360.62197 · doi:10.1214/15-AOS1425
[46] Zhang, C.-H. (2002). Risk bounds in isotonic regression. Ann. Statist.30 528-555. · Zbl 1012.62045 · doi:10.1214/aos/1021379864
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.