logcondens: Estimate a Log-Concave Probability Density from iid Observations. Given independent and identically distributed observations X(1), ..., X(n), this package allows to compute the maximum likelihood estimator (MLE) of a density as well as a smoothed version of it under the assumption that the density is log-concave, see Rufibach (2007) and Duembgen and Rufibach (2009). The main function of the package is ’logConDens’ that allows computation of the log-concave MLE and its smoothed version. In addition, we provide functions to compute (1) the value of the density and distribution function estimates (MLE and smoothed) at a given point (2) the characterizing functions of the estimator, (3) to sample from the estimated distribution, (5) to compute a two-sample permutation test based on log-concave densities, (6) the ROC curve based on log-concave estimates within cases and controls, including confidence intervals for given values of false positive fractions (7) computation of a confidence interval for the value of the true density at a fixed point. Finally, three datasets that have been used to illustrate log-concave density estimation are made available

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  1. Anderson-Bergman, Clifford; Yu, Yaming: Computing the log concave NPMLE for interval censored data (2016)
  2. Mu, Xiaosheng: Log-concavity of a mixture of beta distributions (2015)
  3. Royset, Johannes O.; Wets, Roger J-B: Fusion of hard and soft information in nonparametric density estimation (2015)
  4. Wong, Ting-Kam Leonard: Optimization of relative arbitrage (2015)
  5. Balabdaoui, Fadoua: Global convergence of the log-concave MLE when the true distribution is geometric (2014)
  6. Balabdaoui, Fadoua; Butucea, Cristina: On location mixtures with Pólya frequency components (2014)
  7. Chan, Ngai Hang; Chen, Kun; Yau, Chun Yip: On the Bartlett correction of empirical likelihood for Gaussian long-memory time series (2014)
  8. Dümbgen, Lutz; Rufibach, Kaspar; Schuhmacher, Dominic: Maximum-likelihood estimation of a log-concave density based on censored data (2014)
  9. Durot, Cécile; Lopuhaä, Hendrik P.: A Kiefer-Wolfowitz type of result in a general setting, with an application to smooth monotone estimation (2014)
  10. Chen, Yining; Samworth, Richard J.: Smoothed log-concave maximum likelihood estimation with applications (2013)
  11. Guntuboyina, Adityanand: Optimal rates of convergence for convex set estimation from support functions (2012)
  12. Han, Bing; Dalal, Siddhartha R.: A Bernstein-type estimator for decreasing density with application to $p$-value adjustments (2012)
  13. Meyer, Mary C.: Nonparametric estimation of a smooth density with shape restrictions (2012)
  14. Samworth, Richard J.; Yuan, Ming: Independent component analysis via nonparametric maximum likelihood estimation (2012)
  15. Dümbgen, Lutz; Samworth, Richard; Schuhmacher, Dominic: Approximation by log-concave distributions, with applications to regression (2011)
  16. Hazelton, Martin L.: Assessing log-concavity of multivariate densities (2011)
  17. Cule, Madeleine; Samworth, Richard: Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density (2010)
  18. Dentcheva, Darinka; Penev, Spiridon: Shape-restricted inference for Lorenz curves using duality theory (2010)
  19. Groeneboom, Piet; Jongbloed, Geurt; Witte, Birgit I.: Maximum smoothed likelihood estimation and smoothed maximum likelihood estimation in the current status model (2010)
  20. Koenker, Roger; Mizera, Ivan: Quasi-concave density estimation (2010)

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