logo AFST
Statistics, yokes and symplectic geometry
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 6 (1997) no. 3, pp. 389-427.
@article{AFST_1997_6_6_3_389_0,
     author = {Ole E. Barndorff-Nielsen and Peter E. Jupp},
     title = {Statistics, yokes and symplectic geometry},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {389--427},
     publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences},
     address = {Toulouse},
     volume = {Ser. 6, 6},
     number = {3},
     year = {1997},
     zbl = {0908.62002},
     mrnumber = {1610891},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_1997_6_6_3_389_0/}
}
TY  - JOUR
AU  - Ole E. Barndorff-Nielsen
AU  - Peter E. Jupp
TI  - Statistics, yokes and symplectic geometry
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 1997
SP  - 389
EP  - 427
VL  - 6
IS  - 3
PB  - Université Paul Sabatier. Faculté des sciences
PP  - Toulouse
UR  - https://afst.centre-mersenne.org/item/AFST_1997_6_6_3_389_0/
LA  - en
ID  - AFST_1997_6_6_3_389_0
ER  - 
%0 Journal Article
%A Ole E. Barndorff-Nielsen
%A Peter E. Jupp
%T Statistics, yokes and symplectic geometry
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 1997
%P 389-427
%V 6
%N 3
%I Université Paul Sabatier. Faculté des sciences
%C Toulouse
%U https://afst.centre-mersenne.org/item/AFST_1997_6_6_3_389_0/
%G en
%F AFST_1997_6_6_3_389_0
Ole E. Barndorff-Nielsen; Peter E. Jupp. Statistics, yokes and symplectic geometry. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 6 (1997) no. 3, pp. 389-427. https://afst.centre-mersenne.org/item/AFST_1997_6_6_3_389_0/

[1] Abraham (R.) and Marsden (J.E.) .- Foundations of Mechanics, 2nd ed., Addison-Wesley, Redwood City (1978). | MR | Zbl

[2] Amari (S.-I.) .- Differential-Geometrical Methods in Statistics, Lecture Notes in Statistics, Springer-Verlag, Heidelberg, 28 (1985). | MR | Zbl

[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. | MR | Zbl

[4] Balian (R.) .- From Microphysics, to Macrophysics, Springer-Verlag, Berlin, 1 (1991). | MR | Zbl

[5] Barndorff-Nielsen (O.E.) .- Hyperbolic distributions and distributions on hyperbolae, Scand. J. Statist. 5 (1978), pp. 151-157. | MR | Zbl

[6] Barndorff-Nielsen (O.E.) .- Likelihood and observed geometries, Ann. Statist. 14 (1986), pp. 856-873. | MR | Zbl

[7] Barndorff-Nielsen (O.E.) .- Differential geometry and statistics: some mathematical aspects, Indian J. Math. 29 (1987), pp. 335-350. | MR | Zbl

[8] Barndorff-Nielsen (O.E.) .- Parametric Statistical Models and Likelihood, Lecture Notes in Statistics, Springer-Verlag, Heidelberg, 50 (1988). | MR | Zbl

[9] Barndorff-Nielsen (O.E.) and Cox (D.R.) .- Inference and Asymptotics, Chapman & Hall, London (1994). | Zbl

[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. | MR | Zbl

[11] Barndorff-Nielsen (O.E.) and Jupp (P.E.) .- Yokes and symplectic structures, J. Statist. Planning and Infce. 63 (1997), pp. 133-146. | MR | Zbl

[12] Blæsild (P.) . - Yokes and tensors derived from yokes, Ann. Inst. Statist. Math. 43 (1991), pp. 95-113. | MR | Zbl

[13] Combet (E.) .- Intégrales Exponentielles, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 937 (1982). | MR | Zbl

[14] Critchley (F.), Marriott (P.K.) and Salmon (M.) .- Preferred point geometry and statistical manifolds, Ann. Statist. 21 (1993), 1197-1224. | MR | Zbl

[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. | MR | Zbl

[16] Eguchi (S.) .- Second order efficiency of minimum contrast estimation in a curved exponential family, Ann. Statist. 11 (1983), pp. 793-803. | MR | Zbl

[17] Friedrich (T.) . - Die Fisher-Information und symplectische Strukturen, Math. Nachr. 153 (1991), pp. 273-296. | MR | Zbl

[18] Jensen (J.L.) .- On the hyperboloid distribution, Scand. J. Statist. 8 (1981), pp. 193-206. | MR | Zbl

[19] Marsden (J.E.) .- Lectures on Mechanics, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 174 (1992). | MR | Zbl

[20] Mcduff (D.) .- Examples of symplectic structures, Invent. Math. 89 (1987), pp. 13-36. | MR | Zbl

[21] Murray (M.K.) and Rice (J.W.) .- Differential Geometry and Statistics, Chapman & Hall, London (1993). | Zbl

[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. | MR | Zbl

[23] Nakamura (Y.) .- Gradient systems associated with probability distributions, Japan J. Industr. Appl. Math. 11 (1994), pp. 21-30. | MR | Zbl

[24] Skovgaard (I.M.) .- On the density of minimum contrast estimators, Ann. Statist. 18 (1990), pp. 779-789. | MR | Zbl

[25] Weinstein (A.) .- Symplectic manifolds and their Lagrangian submanifolds, Adv. Math. 6 (1971), pp. 329-346. | MR | Zbl

[26] Weinstein (A.) . - Lectures on Symplectic Manifolds, AMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, Rhode Island, 29 (1977). | MR | Zbl