Publication Cover
Statistics
A Journal of Theoretical and Applied Statistics
Volume 45, 2011 - Issue 3
127
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Inference in ϕ-families of distributions

Pages 223-236 | Received 15 Mar 2008, Accepted 13 Oct 2009, Published online: 23 Feb 2010

References

  • Barndorff-Nielsen , O. 1978 . Information and Exponential Families in Statistical Theory , Chichester : Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons Ltd .
  • Borwein , J. M. and Lewis , A. S. 1991 . Duality relationships for entropy-like minimization problems . SIAM J. Control and Optim. , 29 : 325 – 338 .
  • Borwein , J. M. and Lewis , A. S. 1993 . Partially-finite programming in L 1 and the existence of maximum entropy estimates . SIAM J. Optim. , 3 : 248 – 267 .
  • Borwein , J. M. and Lewis , A. S. 1993 . On the failure of maximum entropy reconstruction for Fredholm equations and other infinite systems . Math. Program. , 63 : 251 – 261 .
  • Dacunha-Castelle , D. and Gamboa , F. 1990 . Maximum d'entropie et problèmes des moments . Ann. Insti. Henri Poincaré B , 26 : 567 – 596 .
  • Decarreau , A. , Hilhorst , D. , Lemaréchal , C. and Navaza , J. 1992 . Dual methods in entropy maximization. Application to some problems in crystallography . SIAM J. on Optim. , 2 : 173 – 197 .
  • Gamboa , F. and Gasiat , E. 1997 . Bayesian methods and maximum entropy for ill-posed inverse problems . Ann. Stat. , 25 : 328 – 350 .
  • Csiszár , I. 1995 . Generalized projections for non-negative functions . Acta Math. Hung. , 68 : 161 – 186 .
  • Léonard , C. 2003 . Minimizers of energy functionals under not very integrable constraints . J. Convex Anal. , 10 : 63 – 88 .
  • Dacunha-Castelle , D. and Gamboa , F. Maximum d'entropie, fonctions de type négatif et généralisation des familles exponentielles , France : Université d'Orsay . Prépublications
  • McCullagh , P. and Nelder , J. A. 1983 . Generalized Linear Models , London : Monographs on Statistics and Applied Probability, Chapman & Hall .
  • Pardo , J. A. and Pardo , M. C. 2008 . Minimum φ-divergence estimator and φ-divergence statistics in generalized linear models with binary data . Meth. Comput. Appl. Probab. , 10 : 357 – 379 .
  • Liese , F. and Vajda , I. 1987 . Convex Statistical Distances Vol. 95 , Leipzig Teubner Texts in Mathematics, BSB B.G. Teubner Verlagsgesellschaft
  • Keziou , A. 2003 . Dual representation of φ-divergence and applications . C. R. Math. Acad. Sci. Paris , 336 : 857 – 862 .
  • Broniatowski , M. and Keziou , A. 2006 . Minimization of φ-divergences on sets of signed measures . Stud. Sci. Math. Hung. , 43 : 403 – 442 .
  • Pardo , L. 2006 . Statistical Inference Based on Divergence Measures , Boca Raton, FL : Chapman & Hall/CRC .
  • Owen , A. B. 1988 . Empirical likelihood ratio confidence intervals for a single functional . Biometrika , 75 : 237 – 249 .
  • Owen , A. B. 2001 . Empirical Likelihood , Boca Raton, FL : Chapman and Hall .
  • Bertail , P. 2006 . Empirical likelihood in some semiparametric models . Bernoulli , 12 : 299 – 331 .
  • Broniatowski , M. 2004 . Estimation of the Kullback-Leibler divergence . Math. Methods Stat. , 12 : 391 – 409 .
  • Rockafellar , R. T. 1970 . Convex Analysis , Princeton, NJ : Princeton University Press .
  • Bredon , G. E. “ Topology and Geometry, Graduate Texts in Mathematics ” . Vol. 139 , New York : Springer-Verlag .
  • Dieudonné , J. 1972 . Eléments d'Analyse , Gauthier-Vilars, Paris : Tome I, Fondements de l'Analyse Moderne .
  • Blot , J. 1991 . On global implicit functions . Nonlinear Anal. Theory Methods Appl. , 17 : 947 – 959 .
  • van der Vaart , A. W. 1998 . Asymptotic Statistics , Cambridge : Cambridge University Press .
  • van de Geer , S. 2000 . Empirical Processes in M-Estimation , Cambridge : Cambridge University Press .
  • Zhang , F. 2005 . The Schur Complement and its Applications , Vol. 4 , New York : Springer-Verlag . Numerical Methods and Algorithms

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.