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Original Articles

An EM algorithm for fitting a mixture model with symmetric log-concave densities

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Pages 78-87 | Received 26 Feb 2018, Accepted 27 Sep 2018, Published online: 22 Dec 2018

References

  • Balabdaoui, F. 2004. Nonparametric estimation of a k-monotone density: A new asymptotic distribution theory. PhD diss., University of Washington.
  • Balabdaoui, F., and C. Butucea. 2014. On location mixtures with Pólya frequency components. Statistics & Probability Letters 95:144–9.
  • Balabdaoui, F., and C. R. Doss. 2018. Inference for a two-component mixture of symmetric distributions under log-concavity. Bernoulli 24 (2):1053–71.
  • Balabdaoui, F., K. Rufibach, and J. A. Wellner. 2009. Limit distribution theory for maximum likelihood estimation of a log-concave density. The Annals of Statistics 37 (3):1299.
  • Bordes, L., D. Chauveau, and P. Vandekerkhove. 2007. A stochastic EM algorithm for a semiparametric mixture model. Computational Statistics & Data Analysis 51 (11):5429–43.
  • Bordes, L., S. Mottelet, and P. Vandekerkhove. 2006. Semiparametric estimation of a two-component mixture model. The Annals of Statistics 34 (3):1204–32.
  • Butucea, C., and P. Vandekerkhove. 2014. Semiparametric mixtures of symmetric distributions. Scandinavian Journal of Statistics 41 (1):227–39.
  • Chang, G. T., and G. Walther. 2007. Clustering with mixtures of log-concave distributions. Computational Statistics & Data Analysis 51 (12):6242–51.
  • Dempster, A., N. Laird, and D. Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological) 39 (1):1–38.
  • Doss, C. R., and J. A. Wellner. 2016. Global rates of convergence of the mles of log-concave and s-concave densities. The Annals of Statistics 44(3):954–81.
  • Doss, C. R., and J. A. Wellner. 2018. Log-concave density estimation with symmetry or modal constraints. arXiv Preprint arXiv 1611:10335v3.
  • Dümbgen, L., and K. Rufibach. 2009. Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency. Bernoulli 15 (1):40–68.
  • Dümbgen, L., R. Samworth, and D. Schuhmacher. 2011. Approximation by log-concave distributions, with applications to regression. The Annals of Statistics 39 (2):702–30.
  • Grenander, U. 1956. On the theory of mortality measurement: Part ii. Scandinavian Actuarial Journal 1956 (2):125–53.
  • Hu, H., Y. Wu, and W. Yao. 2016. Maximum likelihood estimation of the mixture of log-concave densities. Computational Statistics & Data Analysis 101:137–47.
  • Hunter, D. R., S. Wang, and T. P. Hettmansperger. 2007. Inference for mixtures of symmetric distributions. The Annals of Statistics 35 (1):224–51.
  • Khas’minskii. R. 1979. A lower bound on the risks of non-parametric estimates of densities in the uniform metric. Theory of Probability & Its Applications 23 (4):794–8.
  • Kiefer, J. 1953. Sequential minimax search for a maximum. Proceedings of the American Mathematical Society 4 (3):502–6.
  • Pal, J. K., M. Woodroofe, and M. Meyer. 2007. Estimating a polya frequency function2. Lecture Notes-Monograph Series 54:239–49.
  • Rockafellar, R. T. 2015. Convex analysis. Princeton, NJ: Princeton University Press.
  • Rufibach, K. 2006. Log-concave density estimation and bump hunting for IID observations. PhD diss., Universität Bern.
  • Walther, G. 2002. Detecting the presence of mixing with multiscale maximum likelihood. Journal of the American Statistical Association 97 (458):508–13.
  • Wu, C. J. 1983. On the convergence properties of the EM algorithm. The Annals of Statistics 11 (1):95–103.
  • Xu, M., and R. J. Samworth. 2017. High-dimensional nonparametric density estimation via symmetry and shape constraints. Technical report. http://www.statslab.cam.ac.uk/rjs57/Research.html.

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