Finite row-column exchangeable arrays

Bruno Bassan; Marco Scarsini

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 1, page 137-145
  • ISSN: 0010-2628

Abstract

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We generalize well known results about the extendibility of finite exchangeable sequences and provide necessary conditions for finite and infinite extendibility of a finite row-column exchangeable array. These conditions depend in a simple way on the correlation matrix of the array.

How to cite

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Bassan, Bruno, and Scarsini, Marco. "Finite row-column exchangeable arrays." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 137-145. <http://eudml.org/doc/22324>.

@article{Bassan1998,
abstract = {We generalize well known results about the extendibility of finite exchangeable sequences and provide necessary conditions for finite and infinite extendibility of a finite row-column exchangeable array. These conditions depend in a simple way on the correlation matrix of the array.},
author = {Bassan, Bruno, Scarsini, Marco},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {extendibility; partial exchangeability; de Finetti's theorem; extendibility; partial exchangeability},
language = {eng},
number = {1},
pages = {137-145},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Finite row-column exchangeable arrays},
url = {http://eudml.org/doc/22324},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Bassan, Bruno
AU - Scarsini, Marco
TI - Finite row-column exchangeable arrays
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 137
EP - 145
AB - We generalize well known results about the extendibility of finite exchangeable sequences and provide necessary conditions for finite and infinite extendibility of a finite row-column exchangeable array. These conditions depend in a simple way on the correlation matrix of the array.
LA - eng
KW - extendibility; partial exchangeability; de Finetti's theorem; extendibility; partial exchangeability
UR - http://eudml.org/doc/22324
ER -

References

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  1. Aldous D.J., Representations for partially exchangeable arrays of random variables, Journal of Multivariate Analysis 11 (1981), 581-598. (1981) Zbl0474.60044MR0637937
  2. Aldous D.J., Partial exchangeability and d ¯ -topologies, in Koch G. and Spizzichino F. (eds.), Exchangeability in Probability and Statistics, North-Holland, Amsterdam, 1982, pp.23-38. MR0675962
  3. Aldous D.J., On exchangeability and conditional independence, in Koch G. and Spizzichino F. (eds.), Exchangeability in Probability and Statistics, North-Holland, Amsterdam, 1982, pp.65-170. Zbl0493.60021MR0675972
  4. Finetti B., Teoria della Probabilità, Einaudi, Torino, 1970; English translation: {Theory of Probability}, Vols. 1 and 2, Wiley, New York, 1974-75. 
  5. Gaifman H., Concerning measures in first order calculi, Israel Journal of Mathematics 2 (1961), 1-18. (1961) Zbl0192.03302MR0175755
  6. Hoover D.N., Row-column exchangeability and a generalized model for probability, in Koch G. and Spizzichino F. (eds.), Exchangeability in Probability and Statistics, North-Holland, Amsterdam, 1982, pp.81-291. Zbl0495.60040MR0675982
  7. Hoover D.N., Tail fields of partially exchangeable arrays, Journal of Multivariate Analysis 31 (1989), 160-163. (1989) Zbl0683.60027MR1022361
  8. Krauss P.H., Representations of symmetric probability models, Journal of Symbolic Logic 34 (1969), 183-193. (1969) Zbl0218.02022MR0275482
  9. Scarsini M., Verdicchio L., On the extendibility of partially exchangeable vectors, Statistics & Probability Letters 16 (1993), 43-46. (1993) Zbl0764.60041MR1208497
  10. Silverman B.W., Limit theorems for dissociated random variables, Advances in Applied Probability 8, (1976), 806-819. (1976) Zbl0355.60026MR0431348
  11. von Plato J., Finite partial exchangeability, Statistics & Probability Letters 11 (1991), 99-102. (1991) Zbl0727.60038MR1092966

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