Cite

[1] Y. Chen and R. J. Samworth, \Smoothed log-concave maximum likelihood estimation with applications," Statist. Sinica, vol. 23, 2013.10.5705/ss.2011.224Search in Google Scholar

[2] M. Cule, R. Samworth, and M. Stewart, \Maximum likelihood estimation of a multi-dimensional logconcave density," J. R. Stat. Soc. Series B Stat. Methodol., vol. 72, no. 5, pp. 545-607, 2010.10.1111/j.1467-9868.2010.00753.xSearch in Google Scholar

[3] L. Dümbgen and K. Rufibach, \Maximum likelihood estimation of a logconcave density and its distribution function: Basic properties and uniform consistency," Bernoulli, vol. 15, no. 1, pp. 40-68, 2009.10.3150/08-BEJ141Search in Google Scholar

[4] R. Koenker and I. Mizera, \Quasi-concave density estimation," Ann. Stat., vol. 38, no. 5, pp. 2998-3027, 2010.Search in Google Scholar

[5] G. Walther, \Inference and modeling with log-concave distributions," Statist. Sci., vol. 24, no. 3, pp. 319-327, 2009.10.1214/09-STS303Search in Google Scholar

[6] B. Klartag and V. Milman, \Geometry of log-concave functions and measures," Geom. Dedicata, vol. 112, no. 1, pp. 169-182, 2005.10.1007/s10711-004-2462-3Search in Google Scholar

[7] L. Lovász and S. Vempala, \The geometry of log-concave functions and sampling algorithms," Rand. Structures Alg., vol. 30, no. 3, pp. 307-358, 2007.10.1002/rsa.20135Search in Google Scholar

[8] A. Seregin and J. Wellner, \Nonparametric estimation of multivariate convex-transformed densities," Ann. Statistics, vol. 38, no. 6, pp. 3751-3781, 2010.Search in Google Scholar

[9] B. Silverman, \On the estimation of a probability density function by the maximum penalized likelihood method," Ann. Stat., vol. 10, no. 3, pp. 795-810, 1982.10.1214/aos/1176345872Search in Google Scholar

[10] R. Rockafellar and R.-B. Wets, Variational Analysis, vol. 317. Springer, 3rd ed., 2009.Search in Google Scholar

[11] M. Cule, R. Gramacy, and R. Samworth, \LogConcDEAD: An R package for maximum likelihood estimation of a multivariate log-concave density," J. Stat. Softw., vol. 29, no. 2, pp. 1-20, 2009.10.18637/jss.v029.i02Search in Google Scholar

[12] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, 2004.10.1017/CBO9780511804441Search in Google Scholar

[13] F. Rathke, S. Schmidt, and C. Schnörr, \Probabilistic intra-retinal layer segmentation in 3-D OCT images using global shape regularization," Med. Image Anal., vol. 18, no. 5, pp. 781-794, 2014.10.1016/j.media.2014.03.00424835184Search in Google Scholar

eISSN:
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Language:
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Journal Subjects:
Mathematics, General Mathematics