Geodesic
The Law of the Iterated Logarithm for Matrix-Normed Sums of Independent Random Variables and Its Applications
Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 363-369 
V. A. Koval'. The Law of the Iterated Logarithm for Matrix-Normed Sums of Independent Random Variables and Its Applications. Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 363-369. http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, the law of the iterated logarithm in $\mathbb R^d$ for sums of independent random vectors subjected to matrix transformations is studied. Application to multidimensional linear regression is considered.

[1] Buldygin V., Solntsev S., Asymptotic Behaviour of Linearly Transformed Sums of Random Variables, Kluwer, Dordrecht, 1997 | Zbl

[2] Ledoux M., Talagrand M., Probability in Banach Spaces, Springer, Berlin, 1991 | Zbl

[3] Rotar V. I., “Neravnomernaya otsenka skorosti skhodimosti v mnogomernoi tsentralnoi predelnoi teoreme”, Teoriya veroyatn. i ee primen., 15:4 (1970), 647–665 | MR | Zbl

[4] Lankaster P., Teoriya matrits, Nauka, M., 1978

[5] Wittmann R., “A general law of iterated logarithm”, Z. Wahrscheinlichkeit. Verw. Gebiete, 68:4 (1985), 521–543 | DOI | MR | Zbl

[6] Chen X., “On the law of the iterated logarithm for independent Banach space-valued random variables”, Ann. Probab., 21:4 (1993), 1991–2011 | DOI | MR | Zbl

[7] Borovkov A. A., Teoriya veroyatnostei, Nauka, M., 1986 | Zbl

[8] Koval V. O., “Pro zakon povtornogo logarifma dlya gaussovikh poslidovnostei ta iogo zastosuvannya”, Teor. imovirnost. matem. statist., 1996, no. 54, 66–71 | MR | Zbl

[9] Lai T. L., “Some almost sure convergence properties of weighted sums of martingale difference sequences”, Almost Everywhere Convergence, II (Evanston, IL, 1989), Acad. Press, Boston, 1991, 179–190

[10] Lai T. L., Wei C. Z., “A law of the iterated logarithm for double arrays of independent random variables with applications to regression and time series models”, Ann. Probab., 10:2 (1982), 320–335 | DOI | MR | Zbl