Previous |  Up |  Next

Article

Keywords:
extendibility; partial exchangeability; de Finetti's theorem
Summary:
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.
References:
[1] Aldous D.J.: Representations for partially exchangeable arrays of random variables. Journal of Multivariate Analysis 11 (1981), 581-598. MR 0637937 | Zbl 0474.60044
[2] 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
[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. MR 0675972 | Zbl 0493.60021
[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. MR 0175755
[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. MR 0675982 | Zbl 0495.60040
[7] Hoover D.N.: Tail fields of partially exchangeable arrays. Journal of Multivariate Analysis 31 (1989), 160-163. MR 1022361 | Zbl 0683.60027
[8] Krauss P.H.: Representations of symmetric probability models. Journal of Symbolic Logic 34 (1969), 183-193. MR 0275482
[9] Scarsini M., Verdicchio L.: On the extendibility of partially exchangeable vectors. Statistics & Probability Letters 16 (1993), 43-46. MR 1208497
[10] Silverman B.W.: Limit theorems for dissociated random variables. Advances in Applied Probability 8, (1976), 806-819. MR 0431348 | Zbl 0355.60026
[11] von Plato J.: Finite partial exchangeability. Statistics & Probability Letters 11 (1991), 99-102. MR 1092966 | Zbl 0727.60038
Partner of
EuDML logo