Finite row-column exchangeable arrays
Bassan, Bruno ; Scarsini, Marco
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 137-145 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1998-01-01
Classification:  60G09 
@article{118992,
     author = {Bruno Bassan and Marco Scarsini},
     title = {Finite row-column exchangeable arrays},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {137-145},
     zbl = {1039.60039},
     mrnumber = {1622998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118992}
}

Bassan, Bruno; Scarsini, Marco. Finite row-column exchangeable arrays. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 137-145. http://gdmltest.u-ga.fr/item/118992/

Aldous D.J. Representations for partially exchangeable arrays of random variables, Journal of Multivariate Analysis 11 (1981), 581-598. (1981) | MR 0637937 | Zbl 0474.60044

Aldous D.J. Partial exchangeability and $\bar d$-topologies, in Koch G. and Spizzichino F. (eds.), Exchangeability in Probability and Statistics, North-Holland, Amsterdam, 1982, pp.23-38. | MR 0675962

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. | MR 0675972 | Zbl 0493.60021

Finetti B. Teoria della Probabilità, Einaudi, Torino, 1970; English translation: {Theory of Probability}, Vols. 1 and 2, Wiley, New York, 1974-75.

Gaifman H. Concerning measures in first order calculi, Israel Journal of Mathematics 2 (1961), 1-18. (1961) | MR 0175755

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. | MR 0675982 | Zbl 0495.60040

Hoover D.N. Tail fields of partially exchangeable arrays, Journal of Multivariate Analysis 31 (1989), 160-163. (1989) | MR 1022361 | Zbl 0683.60027

Krauss P.H. Representations of symmetric probability models, Journal of Symbolic Logic 34 (1969), 183-193. (1969) | MR 0275482

Scarsini M.; Verdicchio L. On the extendibility of partially exchangeable vectors, Statistics & Probability Letters 16 (1993), 43-46. (1993) | MR 1208497

Silverman B.W. Limit theorems for dissociated random variables, Advances in Applied Probability 8, (1976), 806-819. (1976) | MR 0431348 | Zbl 0355.60026

Von Plato J. Finite partial exchangeability, Statistics & Probability Letters 11 (1991), 99-102. (1991) | MR 1092966 | Zbl 0727.60038