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On the almost sure central limit theorems for the vectors of several large maxima and for some random permanents

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EN
Abstrakty
EN
In our paper we prove two kinds of the so-called almost sure central limit theorem (ASCLT). The first one is the ASCLT for the vectors ((Mn(1) , . . . ,Mn(r)), where Mn(j) n - the j-th largest maximum of X1, . . . ,Xn and {Xi} is an i.i.d. sequence. Our second result is the ASCLT for some random permanents.
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Rocznik
Strony
949--963
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
  • Department of Econometrics and Computer Science Faculty of Statistics and Econometrics Warsaw Agricultural University ul. Nowoursynowska 159 bud. 34 02-787 Warszawa, Poland, mdudzinski@mors.sggw.waw.pl
Bibliografia
  • [1] I. Berkes and E. Csaki, A universal result in almost sure central limit theory, Stoch. Process. Appl. 94 (2001), 105-134.
  • [2] I. Berkes and H. Dehling, Some limit theorems in log density, Ann. Probab. 21 (1993), 1640-1670.
  • [3] G. Brosamler, An almost everywhere central limit theorem, Math. Proc. Cambridge Philos. Soc. 104 (1988), 561-574.
  • [4] S. Cheng, L. Peng and Y. Qi, Almost sure convergence in extreme value theory, Math. Nachr. 190 (1998), 43-50.
  • [5] E. Csaki and K. Gonchigdanzan, Almost sure limit theorems for the maximum of stationary Gaussian sequences, Statist. Probab. Lett. 58 (2002), 195-203.
  • [6] M. Dudziński, An almost sure maximum limit theorem for certain class of dependent stationary Gaussian sequences, Demonstratio Math. 35 (2002), 879-890.
  • [7] M. Dudziński, A note on the almost sure central limit theorem for some dependent random variables, Statist. Probab. Lett. 61 (2003), 31-40.
  • [8] M. Dudziński, An almost sure limit theorem for the maxima and sums of stationary Gaussian sequences, Probab. Math. Statist. 23 (2003), 139-152.
  • [9] I. Fahrner and U. Stadtmueller, On almost sure max-limit theorems, Statist. Probab. Lett. 37 (1998), 229-236.
  • [10] A. Fisher, A pathwise central limit theorem for random walks, preprint.
  • [11] M. Lacey and W. Philipp, A note on the almost sure central limit theorem, Statist. Probab. Lett. 9 (1990), 201-205.
  • [12] M. R. Leadbetter, G. Lindgren and H. Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, New York, Heidelberg, Berlin (1983).
  • [13] P. Matula, Convergence of weighted averages of associated random variables, Probab. Math. Statist. 16 (1996), 337-343.
  • [14] P. Matula, On the almost sure central limit theorem for associated random variables, Probab. Math. Statist. 18 (1998), 411-416.
  • [15] M. Peligrad and Q. Shao, A note on the almost sure central limit theorem for weakly dependent random variables, Statist. Probab. Lett. 22 (1995), 131-136.
  • [16] G. A. Rempa la and J.Wesołowski, Central limit theorems for random permanents with correlation structure, J. Theoret. Probab. 15 (2002), 63-76.
  • [17] P. Schatte, On strong versions of the central limit theorem, Math. Nachr. 137 (1988), 249-256.
  • [18] U. Stadtmueller, Almost sure versions of distributional limit theorems for certain order statistics, Statist. Probab. Lett. 58 (2002), 413-426.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0018-0022
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