Geodesic
Maximum likelihood method in de Finetti's theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 808-816 Cet article a éte moissonné depuis la source Math-Net.Ru

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De Finetti's theorem states that the elements of an infinite exchangeable sequence of random variables are conditionally independent and identically distributed relative to some random variable (or a sigma-algebra generated by that random variable). In this work, we construct this random variable using the maximum likelihood method.
Keywords: de Finetti's theorem, conditional independence, maximum likelihood estimate, sufficient statistic, Gaussian measures on Hilbert spaces. 
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L. E. Melkumova; S. Ya. Shatskikh. Maximum likelihood method in de Finetti's theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 808-816. http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a9/

[1] Yuan Shih Chow, H. Teicher, Probability theory. Independence, interchangeability, martingales, Springer Texts Statist., 3rd ed., Springer-Verlag, New York–Heidelberg, 2003, xxii+488 pp. | DOI | MR | Zbl

[2] J. F. C. Kingman, “Uses of exchangeability”, Ann. Probability, 6:2 (1978), 183–197 | DOI | MR | Zbl

[3] E. M. Knutova, S. Ya. Shatskikh, “Asymptotic properties of conditional quantiles for a class of symmetric distributions”, Theory Probab. Appl., 51:2 (2007), 350–358 | DOI | DOI | MR | Zbl

[4] T. S. Ferguson, A course in large sample theory, Texts Statist. Sci. Ser., Chapman Hall, London, 1996, x+245 pp. | MR | Zbl

[5] A. W. van der Vaart, Asymptotic statistics, Camb. Ser. Stat. Probab. Math., 3, paperback ed., Cambridge University Press, Cambridge, 2000, xvi+443 pp. | DOI | MR | Zbl

[6] I. A. Ibragimov, R. Z. Has'minskiĭ, Statistical estimation. Asymptotic theory, Appl. Math., 16, Springer-Verlag, New York–Berlin, 1981, vii+403 pp. | MR | MR | Zbl | Zbl

[7] V. I. Bogachev, Gaussian measures, Math. Surveys Monogr., 62, Amer. Math. Soc., Providence, RI, 1998, xii+433 pp. | DOI | MR | MR | Zbl | Zbl

[8] A. N. Shiryaev, “Probability”, Grad. Texts in Math., 95, 2nd ed., Springer-Verlag, New York, 1996, xvi+623 pp. | DOI | MR | Zbl