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

References in zbMATH (referenced in 46 articles , 1 standard article )

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  1. Groeneboom, Piet; Jongbloed, Geurt: Some developments in the theory of shape constrained inference (2018)
  2. Kim, Arlene K. H.; Guntuboyina, Adityanand; Samworth, Richard J.: Adaptation in log-concave density estimation (2018)
  3. Samworth, Richard J.: Recent progress in log-concave density estimation (2018)
  4. Wang, Tengyao; Samworth, Richard J.: High dimensional change point estimation via sparse projection (2018)
  5. Dümbgen, Lutz; Kolesnyk, Petro; Wilke, Ralf A.: Bi-log-concave distribution functions (2017)
  6. Anderson-Bergman, Clifford; Yu, Yaming: Computing the log concave NPMLE for interval censored data (2016)
  7. Baraud, Y.; Birgé, L.: Rho-estimators for shape restricted density estimation (2016)
  8. Doss, Charles R.; Wellner, Jon A.: Global rates of convergence of the MLEs of log-concave and (s)-concave densities (2016)
  9. Han, Qiyang; Wellner, Jon A.: Approximation and estimation of (s)-concave densities via Rényi divergences (2016)
  10. Chen, Yining: Semiparametric time series models with log-concave innovations: maximum likelihood estimation and its consistency (2015)
  11. Mu, Xiaosheng: Log-concavity of a mixture of beta distributions (2015)
  12. Royset, Johannes O.; Wets, Roger J.-B.: Fusion of hard and soft information in nonparametric density estimation (2015)
  13. Söhl, Jakob: Uniform central limit theorems for the Grenander estimator (2015)
  14. Wong, Ting-Kam Leonard: Optimization of relative arbitrage (2015)
  15. Azadbakhsh, Mahdis; Jankowski, Hanna; Gao, Xin: Computing confidence intervals for log-concave densities (2014)
  16. Balabdaoui, Fadoua: Global convergence of the log-concave MLE when the true distribution is geometric (2014)
  17. Balabdaoui, Fadoua; Butucea, Cristina: On location mixtures with Pólya frequency components (2014)
  18. Chan, Ngai Hang; Chen, Kun; Yau, Chun Yip: On the Bartlett correction of empirical likelihood for Gaussian long-memory time series (2014)
  19. Dümbgen, Lutz; Rufibach, Kaspar; Schuhmacher, Dominic: Maximum-likelihood estimation of a log-concave density based on censored data (2014)
  20. Durot, Cécile; Lopuhaä, Hendrik P.: A Kiefer-Wolfowitz type of result in a general setting, with an application to smooth monotone estimation (2014)

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