Free Access
Volume 18, 2014
Page(s) 332 - 341
Published online 03 October 2014
  1. A. Barron, M.J. Schervish and L. Wasserman, The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27 (1999) 536–561. [CrossRef] [MathSciNet] [Google Scholar]
  2. N. Choudhuri, S. Ghosal and A. Roy, Bayesian estimation of the spectral density of a time series. J. Amer. Statist. Assoc. 99 (2004) 1050–1059. [CrossRef] [MathSciNet] [Google Scholar]
  3. P. Diaconis and D. Freedman, On the consistency of Bayes estimates. With a discussion and a rejoinder by the authors. Ann. Statist. 14 (1986) 1–67. [CrossRef] [MathSciNet] [Google Scholar]
  4. V. Genon-Catalot and J. Jacod, On the estimation of the diffusion coefficient for multi-dimensional diffusion processes. Ann. Inst. Henri Poincaré Probab. Statist. 29 (1993) 119–151. [Google Scholar]
  5. V. Genon-Catalot, C. Laredo and D. Picard, Nonparametric estimation of the diffusion coefficient by wavelets methods. Scand. J. Statist. 19 (1992) 317–335. [MathSciNet] [Google Scholar]
  6. S. Ghosal, J.K. Ghosh and R.V. Ramamoorthi, Consistency issues in Bayesian nonparametrics. Asymptotics, Nonparametrics, and Time Series. Vol. 158 of Textbooks Monogr. Dekker, New York (1999) 639–667. [Google Scholar]
  7. S. Ghosal and Y. Tang, Bayesian consistency for Markov processes. Sankhyā 68 (2006) 227–239. [MathSciNet] [Google Scholar]
  8. S. Gugushvili and P. Spreij, Non-parametric Bayesian drift estimation for stochastic differential equations (2012). Preprint arXiv:1206.4981 [math.ST]. [Google Scholar]
  9. M. Hoffmann, Minimax estimation of the diffusion coefficient through irregular samplings. Statist. Probab. Lett. 32 (1997) 11–24. [CrossRef] [MathSciNet] [Google Scholar]
  10. I.A. Ibragimov and R.Z. Has′minskiĭ, Asimptoticheskaya teoriya otsenivaniya [Asymptotic Theory of Estimation] (Russian). Nauka, Moscow (1979). [Google Scholar]
  11. F. van der Meulen, M. Schauer and H. van Zanten, Reversible jump MCMC for nonparametric drift estimation for diffusion processes. Comput. Statist. Data Anal. 71 (2014) 615–632. Available on [CrossRef] [MathSciNet] [Google Scholar]
  12. F.H. van der Meulen, A.W. van der Vaart and J.H. van Zanten, Convergence rates of posterior distributions for Brownian semimartingale models. Bernoulli 12 (2006) 863–888. [CrossRef] [MathSciNet] [Google Scholar]
  13. F. van der Meulen and H. van Zanten, Consistent nonparametric Bayesian estimation for discretely observed scalar diffusions. Bernoulli 19 (2013) 44–63. [CrossRef] [MathSciNet] [Google Scholar]
  14. L. Panzar and H. van Zanten, Nonparametric Bayesian inference for ergodic diffusions. J. Statist. Plann. Inference 139 (2009) 4193–4199. [CrossRef] [MathSciNet] [Google Scholar]
  15. O. Papaspiliopoulos, Y. Pokern, G.O. Roberts and A.M. Stuart, Nonparametric estimation of diffusions: a differential equations approach. Biometrika 99 (2012) 511–531. [CrossRef] [Google Scholar]
  16. G.A. Pavliotis, Y. Pokern and A.M. Stuart, Parameter estimation for multiscale diffusions: an overview. Statistical Methods for Stochastic Differential Equations. Vol. 124 of Monogr. Statist. Appl. Probab. CRC Press, Boca Raton, FL (2012) 429–472. [Google Scholar]
  17. Y. Pokern, A.M. Stuart and J.H. van Zanten. Posterior consistency via precision operators for nonparametric drift estimation in SDEs. Stoch. Process. Appl. 123 (2013) 603–628. [CrossRef] [Google Scholar]
  18. L. Schwartz, On Bayes procedures. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 4 (1965) 10–26. [CrossRef] [MathSciNet] [Google Scholar]
  19. P. Soulier, Nonparametric estimation of the diffusion coefficient of a diffusion process. Stochastic Anal. Appl. 16 (1998) 185–200. [CrossRef] [MathSciNet] [Google Scholar]
  20. A.W. van der Vaart, Asymptotic Statistics. Vol. 3 of Cambr. Ser. Stat. Probab. Math. Cambridge University Press, Cambridge (1998). [Google Scholar]
  21. A.W. van der Vaart and J.H. van Zanten, Rates of contraction of posterior distributions based on Gaussian process priors. Ann. Statist. 36 (2008a) 1435–1463. [CrossRef] [MathSciNet] [Google Scholar]
  22. A.W. van der Vaart and J.H. van Zanten, Reproducing kernel Hilbert spaces of Gaussian priors. Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh. Vol. 3 of Inst. Math. Stat. Collect. Inst. Math. Statist., Beachwood, OH (2008) 200–222. [Google Scholar]
  23. S. Walker, On sufficient conditions for Bayesian consistency. Biometrika 90 (2003) 482–488. [CrossRef] [Google Scholar]
  24. S. Walker, New approaches to Bayesian consistency. Ann. Statist. 32 (2004) 2028–2043. [CrossRef] [MathSciNet] [Google Scholar]
  25. L. Wasserman, Asymptotic properties of nonparametric Bayesian procedures. Practical Nonparametric and Semiparametric Bayesian Statistics. Vol. 133 of Lect. Notes Statist. Springer, New York (1998) 293–304. [Google Scholar]
  26. H. van Zanten, Nonparametric Bayesian methods for one-dimensional diffusion models. Math. Biosci. (2013). Available on [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.