logcondens

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 36 articles )

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  1. Dümbgen, Lutz; Kolesnyk, Petro; Wilke, Ralf A.: Bi-log-concave distribution functions (2017)
  2. Anderson-Bergman, Clifford; Yu, Yaming: Computing the log concave NPMLE for interval censored data (2016)
  3. Baraud, Y.; Birgé, L.: Rho-estimators for shape restricted density estimation (2016)
  4. Doss, Charles R.; Wellner, Jon A.: Global rates of convergence of the MLEs of log-concave and $s$-concave densities (2016)
  5. Han, Qiyang; Wellner, Jon A.: Approximation and estimation of $s$-concave densities via Rényi divergences (2016)
  6. Chen, Yining: Semiparametric time series models with log-concave innovations: maximum likelihood estimation and its consistency (2015)
  7. Mu, Xiaosheng: Log-concavity of a mixture of beta distributions (2015)
  8. Royset, Johannes O.; Wets, Roger J.-B.: Fusion of hard and soft information in nonparametric density estimation (2015)
  9. Söhl, Jakob: Uniform central limit theorems for the Grenander estimator (2015)
  10. Wong, Ting-Kam Leonard: Optimization of relative arbitrage (2015)
  11. Balabdaoui, Fadoua: Global convergence of the log-concave MLE when the true distribution is geometric (2014)
  12. Balabdaoui, Fadoua; Butucea, Cristina: On location mixtures with Pólya frequency components (2014)
  13. Chan, Ngai Hang; Chen, Kun; Yau, Chun Yip: On the Bartlett correction of empirical likelihood for Gaussian long-memory time series (2014)
  14. Dümbgen, Lutz; Rufibach, Kaspar; Schuhmacher, Dominic: Maximum-likelihood estimation of a log-concave density based on censored data (2014)
  15. Durot, Cécile; Lopuhaä, Hendrik P.: A Kiefer-Wolfowitz type of result in a general setting, with an application to smooth monotone estimation (2014)
  16. Saumard, Adrien; Wellner, Jon A.: Log-concavity and strong log-concavity: a review (2014)
  17. Chen, Yining; Samworth, Richard J.: Smoothed log-concave maximum likelihood estimation with applications (2013)
  18. Guntuboyina, Adityanand: Optimal rates of convergence for convex set estimation from support functions (2012)
  19. Han, Bing; Dalal, Siddhartha R.: A Bernstein-type estimator for decreasing density with application to $p$-value adjustments (2012)
  20. Meyer, Mary C.: Nonparametric estimation of a smooth density with shape restrictions (2012)

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