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All issues Volume 17 (2013) ESAIM: PS, 17 (2013) 419-431 References
Free Access
Issue
ESAIM: PS
Volume 17, 2013
Page(s) 419 - 431
DOI https://doi.org/10.1051/ps/2012004
Published online 21 May 2013
  1. I.A. Ahmad and P.E. Lin, A nonparametric estimation of the entropy for absolutely continuous distributions. IEEE Trans. Inf. Theory 22 (1976) 372–375. [CrossRef] [Google Scholar]
  2. I.A. Ahmad and P.E. Lin, A nonparametric estimation of the entropy for absolutely continuous distributions. IEEE Trans. Inf. Theory 36 (1989) 688–692. [CrossRef] [Google Scholar]
  3. C. Andrieu and J. Thoms, A tutorial on adaptive MCMC. Stat. Comput. 18 (2008) 343–373. [CrossRef] [Google Scholar]
  4. Y.F. Atchadé and J. Rosenthal, On adaptive Markov chain Monte Carlo algorithms. Bernoulli 11 (2005) 815–828. [CrossRef] [MathSciNet] [Google Scholar]
  5. P. Billingsley, Probability and Measure, 3rd edition. Wiley, New York (2005). [Google Scholar]
  6. D. Chauveau and P. Vandekerkhove, Improving convergence of the Hastings-Metropolis algorithm with an adaptive proposal. Scand. J. Stat. 29 (2002) 13–29. [CrossRef] [Google Scholar]
  7. D. Chauveau and P. Vandekerkhove, A Monte Carlo estimation of the entropy for Markov chains. Methodol. Comput. Appl. Probab. 9 (2007) 133–149. [CrossRef] [Google Scholar]
  8. Y.G. Dmitriev and F.P. Tarasenko, On the estimation of functionals of the probability density and its derivatives. Theory Probab. Appl. 18 (1973) 628–633. [CrossRef] [Google Scholar]
  9. Y.G. Dmitriev and F.P. Tarasenko, On a class of non-parametric estimates of non-linear functionals of density. Theory Probab. Appl. 19 (1973) 390–394. [CrossRef] [Google Scholar]
  10. R. Douc, A. Guillin, J.M. Marin and C.P. Robert, Convergence of adaptive mixtures of importance sampling schemes. Ann. Statist. 35 (2007) 420–448. [CrossRef] [MathSciNet] [Google Scholar]
  11. E.J. Dudevicz and E.C. Van Der Meulen Entropy-based tests of uniformity. J. Amer. Statist. Assoc. 76 (1981) 967–974. [CrossRef] [MathSciNet] [Google Scholar]
  12. P.P.B. Eggermont and V.N. LaRiccia, Best asymptotic normality of the Kernel density entropy estimator for Smooth densities. IEEE Trans. Inf. Theory 45 (1999) 1321–1326. [CrossRef] [Google Scholar]
  13. W.R. Gilks, S. Richardson and D.J. Spiegelhalter, Markov Chain Monte Carlo in practice. Chapman & Hall, London (1996) [Google Scholar]
  14. W.R. Gilks, G.O. Roberts and S.K. Sahu, Adaptive Markov chain Monte carlo through regeneration. J. Amer. Statist. Assoc. 93 (1998) 1045–1054. [CrossRef] [MathSciNet] [Google Scholar]
  15. L. Györfi and E.C. Van Der Meulen, Density-free convergence properties of various estimators of the entropy. Comput. Statist. Data Anal. 5 (1987) 425–436. [CrossRef] [MathSciNet] [Google Scholar]
  16. L. Györfi and E.C. Van Der Meulen, An entropy estimate based on a Kernel density estimation, Limit Theorems in Probability and Statistics Pécs (Hungary). Colloquia Mathematica societatis János Bolyai 57 (1989) 229–240. [Google Scholar]
  17. H. Haario, E. Saksman and J. Tamminen, An adaptive metropolis algorithm. Bernouilli 7 (2001) 223–242. [Google Scholar]
  18. W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 (1970) 97–109. [Google Scholar]
  19. L. Holden, Geometric convergence of the Metropolis-Hastings simulation algorithm. Statist. Probab. Lett. 39 (1998). [Google Scholar]
  20. A.V. Ivanov and M.N. Rozhkova, Properties of the statistical estimate of the entropy of a random vector with a probability density (in Russian). Probl. Peredachi Inform. 17 (1981) 33–43. Translated into English in Probl. Inf. Transm. 17 (1981) 171–178. [Google Scholar]
  21. S.F. Jarner and E. Hansen, Geometric ergodicity of metropolis algorithms. Stoc. Proc. Appl. 85 (2000) 341–361. [Google Scholar]
  22. K.L. Mengersen and R.L. Tweedie, Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24 (1996) 101–121. [CrossRef] [MathSciNet] [Google Scholar]
  23. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller, Equations of state calculations by fast computing machines. J. Chem. Phys. 21 (1953) 1087–1092. [NASA ADS] [CrossRef] [Google Scholar]
  24. A. Mokkadem, Estimation of the entropy and information of absolutely continuous random variables. IEEE Trans. Inf. Theory 23 (1989) 95–101. [Google Scholar]
  25. R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org (2010), ISBN 3-900051-07-0. [Google Scholar]
  26. G.O. Roberts and J.S. Rosenthal, Optimal scaling for various Metropolis-Hastings algorithms. Statist. Sci. 16 (2001) 351–367. [CrossRef] [MathSciNet] [Google Scholar]
  27. G.O. Roberts and R.L. Tweedie, Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83 (1996) 95–110. [CrossRef] [MathSciNet] [Google Scholar]
  28. D. Scott, Multivariate Density Estimation: Theory, Practice and Visualization. John Wiley, New York (1992). [Google Scholar]
  29. F.P. Tarasenko, On the evaluation of an unknown probability density function, the direct estimation of the entropy from independent observations of a continuous random variable and the distribution-free entropy test of goodness-of-fit. Proc. IEEE 56 (1968) 2052–2053. [CrossRef] [Google Scholar]

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