Statistics, yokes and symplectic geometry

Ole E. Barndorff-Nielsen; Peter E. Jupp

Annales de la Faculté des sciences de Toulouse : Mathématiques (1997)

  • Volume: 6, Issue: 3, page 389-427
  • ISSN: 0240-2963

How to cite

top

Barndorff-Nielsen, Ole E., and Jupp, Peter E.. "Statistics, yokes and symplectic geometry." Annales de la Faculté des sciences de Toulouse : Mathématiques 6.3 (1997): 389-427. <http://eudml.org/doc/73427>.

@article{Barndorff1997,
author = {Barndorff-Nielsen, Ole E., Jupp, Peter E.},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {expected likelihood yoke; Hamiltonian; Lagrangian submanifold; Lie group actions; observed likelihood yoke; raising and lowering tensors; symplectic structures; Lagrangian of a yoke; momentum maps},
language = {eng},
number = {3},
pages = {389-427},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Statistics, yokes and symplectic geometry},
url = {http://eudml.org/doc/73427},
volume = {6},
year = {1997},
}

TY - JOUR
AU - Barndorff-Nielsen, Ole E.
AU - Jupp, Peter E.
TI - Statistics, yokes and symplectic geometry
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1997
PB - UNIVERSITE PAUL SABATIER
VL - 6
IS - 3
SP - 389
EP - 427
LA - eng
KW - expected likelihood yoke; Hamiltonian; Lagrangian submanifold; Lie group actions; observed likelihood yoke; raising and lowering tensors; symplectic structures; Lagrangian of a yoke; momentum maps
UR - http://eudml.org/doc/73427
ER -

References

top
  1. [1] Abraham ( R.) and Marsden ( J.E.) .— Foundations of Mechanics, 2nd ed., Addison-Wesley, Redwood City (1978). Zbl0393.70001MR515141
  2. [2] Amari ( S.-I.) .— Differential-Geometrical Methods in Statistics, Lecture Notes in Statistics, Springer-Verlag, Heidelberg, 28 (1985). Zbl0559.62001MR788689
  3. [3] ARNOL'D ( V.I.) and GIVENTAL' ( A.B.) .— Symplectic Geometry, In "Dynamical Systems IV: Symplectic Geometry and its Applications", Encyclopaedia of Mathematical Sciences (V. I. Arnol'd and S. P. Novikov, eds), Springer-Verlag, Berlin, 4 (1990), pp. 1-136. Zbl0780.58016MR1042758
  4. [4] Balian ( R.) .— From Microphysics, to Macrophysics, Springer-Verlag, Berlin, 1 (1991). Zbl1131.82300MR1129462
  5. [5] Barndorff-Nielsen ( O.E.) .— Hyperbolic distributions and distributions on hyperbolae, Scand. J. Statist.5 (1978), pp. 151-157. Zbl0386.60018MR509451
  6. [6] Barndorff-Nielsen ( O.E.) .— Likelihood and observed geometries, Ann. Statist.14 (1986), pp. 856-873. Zbl0632.62028MR856794
  7. [7] Barndorff-Nielsen ( O.E.) .— Differential geometry and statistics: some mathematical aspects, Indian J. Math.29 (1987), pp. 335-350. Zbl0663.62013MR971645
  8. [8] Barndorff-Nielsen ( O.E.) .— Parametric Statistical Models and Likelihood, Lecture Notes in Statistics, Springer-Verlag, Heidelberg, 50 (1988). Zbl0691.62002MR971982
  9. [9] Barndorff-Nielsen ( O.E.) and Cox ( D.R.) .— Inference and Asymptotics, Chapman & Hall, London (1994). Zbl0826.62004
  10. [10] Barndorff-Nielsen ( O.E.) and Jupp ( P.E.) .- Differential geometry, profile likelihood, L-sufficiency and composite transformation models, Ann. Statist.16 (1988), pp. 1009-1043. Zbl0702.62032MR959187
  11. [11] Barndorff-Nielsen ( O.E.) and Jupp ( P.E.) .— Yokes and symplectic structures, J. Statist. Planning and Infce. 63 (1997), pp. 133-146. Zbl0943.37027MR1491574
  12. [12] Blæsild ( P.) . — Yokes and tensors derived from yokes, Ann. Inst. Statist. Math.43 (1991), pp. 95-113. Zbl0782.62007MR1105824
  13. [13] Combet ( E.) .— Intégrales Exponentielles, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 937 (1982). Zbl0489.58002MR665746
  14. [14] Critchley ( F.), Marriott ( P.K.) and Salmon ( M.) .— Preferred point geometry and statistical manifolds, Ann. Statist.21 (1993), 1197-1224. Zbl0798.62009MR1241265
  15. [15] Critchley ( F.), Marriott ( P.K.) and Salmon ( M.) .— Preferred point geometry and the local differential geometry of the Kullback-Leibler divergence, Ann. Statist.22 (1994), pp. 1587-1602. Zbl0821.62004MR1311991
  16. [16] Eguchi ( S.) .— Second order efficiency of minimum contrast estimation in a curved exponential family, Ann. Statist.11 (1983), pp. 793-803. Zbl0519.62027MR707930
  17. [17] Friedrich ( T.) . — Die Fisher-Information und symplectische Strukturen, Math. Nachr.153 (1991), pp. 273-296. Zbl0792.62003MR1131949
  18. [18] Jensen ( J.L.) .— On the hyperboloid distribution, Scand. J. Statist.8 (1981), pp. 193-206. Zbl0477.62005MR642800
  19. [19] Marsden ( J.E.) .— Lectures on Mechanics, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 174 (1992). Zbl0744.70004MR1171218
  20. [20] Mcduff ( D.) .— Examples of symplectic structures, Invent. Math.89 (1987), pp. 13-36. Zbl0625.53040MR892186
  21. [21] Murray ( M.K.) and Rice ( J.W.) .— Differential Geometry and Statistics, Chapman & Hall, London (1993). Zbl0804.53001
  22. [22] Nakamura ( Y.) . — Completely integrable gradient systems on the manifolds of Gaussian and multinomial distributions, Japan J. Industr. Appl. Math.10 (1993), pp. 179-189. Zbl0814.58021MR1227728
  23. [23] Nakamura ( Y.) .— Gradient systems associated with probability distributions, Japan J. Industr. Appl. Math.11 (1994), pp. 21-30. Zbl0811.58036MR1266518
  24. [24] Skovgaard ( I.M.) .— On the density of minimum contrast estimators, Ann. Statist.18 (1990), pp. 779-789. Zbl0709.62029MR1056336
  25. [25] Weinstein ( A.) .— Symplectic manifolds and their Lagrangian submanifolds, Adv. Math.6 (1971), pp. 329-346. Zbl0213.48203MR286137
  26. [26] Weinstein ( A.) . — Lectures on Symplectic Manifolds, AMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, Rhode Island, 29 (1977). Zbl0406.53031MR464312

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.