100
Views
4
CrossRef citations to date
0
Altmetric
Articles

Asymptotic expansion of the risk of maximum likelihood estimator with respect to α-divergence

Pages 4059-4087 | Received 10 Jan 2017, Accepted 09 Sep 2017, Published online: 13 Nov 2017

References

  • Amari, S. 1985. Differential-geometrical methods in statistics. Lecture Notes in Statistics 28. Heidelberg: Springer-Verlag.
  • Amari, S. 2009. Alpha divergence is unique, belonging to both classes of f-divergence and Bregman divergence. IEEE Transactions on Information Theory 55:4925–31.
  • Amari, S., and A. Chichocki. 2010. Information geometry of divergence function. Bulletin of the Polish Academy of Sciences: Technical Sciences 58:183–95.
  • Amari, S., and H. Nagaoka. 2000. Methods of information geometry. Translations of Mathematical Monographs 191. Rhode Island: American Mathematical Society.
  • Calin, O., and C. Udrişte. 2014. Geometric modeling in probability and statistics. New York: Springer.
  • Corcuera, J., and F. Giummolè. 1999. On the relationship between alpha connections and the asymptotic properties of predictive distributions. Bernoulli 5:163–76.
  • Eguchi, S. 1985. A differential geometric approach to statistical inference on the basis of contrast functionals. Hiroshima Mathematical Journal 15:341–91.
  • Eguchi, S.. 1991. Geometry of minimum contrast. Hiroshima Mathematical Journal 22:631–47.
  • Eguchi, S., and T. Yanagimoto. 2008. Asymptotical improvement of maximum likelihood estimators on Kullback-Leibler loss. Journal of Statistical Planning and Inference 138:3502–11.
  • Komaki, F. 1996. On asymptotic properties of predictive distributions. Biometrika 83:299–313.
  • Maji, P. 2009. F-information measures for efficient selection of discriminative genes from microarray data. IEEE Transactions on Biomedical Engineering 56:1063–9.
  • Murray, M. K., and J. W. Rice. 1993. Differential geometry and statistics. London: Chapman.
  • Qiao, Y., and N Minematsu. 2010. A study on invariance of f-divergence and its application to speech recognition. IEEE Transactions on Signal Processing 58:3884–90.
  • Sheena, Y. 2017. Asymptotic expansion of the risk of maximum likelihood estimator with respect to α-divergence as a measure of the difficulty of specifying a parametric model—with detailed proof. arXiv:1510.08226 [math.ST].
  • Vajda, I. 1989. Theory of statistical inference and information. Dordrecht: Kluwer Academic Publishers.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.