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A note on the almost sure convergence of central order statistics

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Języki publikacji
EN
Abstrakty
EN
We prove almost sure versions of distributional limit theorems for central order statistics. We develop a new method which not only gives a simplified proof of existing results in the literature, but also extends them for general summation methods, leading to considerably sharper results.
Rocznik
Strony
317--329
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • Institute of Statistics, Graz University of Technology, Steyrergasse 17/IV, 8010 Graz, Austria
Bibliografia
  • [1] M. Atlagh, Théorème central limite presque sûr et loi du logarithme itéré pour des sommes de variables aléatoires indépendantes, C. R. Acad. Sci. Paris Sér. I. 316 (1993), pp. 929-933.
  • [2] M. Atlagh and M. Weber, Le théorème central limite presque sûr, Expo. Math. 18 (2000), pp. 97-126.
  • [3] I. Berkes, Results and problems related to the pointwise central limit theorem, in: Asymptotic Methods in Probability and Statistics (Ottawa, ON, 1997), North-Holland, Amsterdam 1998, pp. 59-96.
  • [4] I. Berkes and E. Csáki, A universal result in almost sure central limit theory, Stochastic Process. Appl. 94 (2001), pp. 105-134.
  • [5] I. Berkes and W. Philipp, Approximation theorems for independent and weakly dependent random vectors, Ann. Probab. 7 (1979), pp. 29-54.
  • [6] G. A. Brosamler, An almost everywhere central limit theorem, Math. Proc. Cambridge Philos. Soc. 104 (1988), pp. 561-574.
  • [7] K. Chandrasekharan and S. Minakshisundaram, Typical Meam, Oxford University Press, 1952.
  • [8] S. Cheng, L. Peng and Y. Qi, Almost sure convergence in extreme value theory, Math. Nachr. 190 (1998), pp. 43-50.
  • [9] R. M. Dudley, Real Analysis and Probability, Cambridge Stud. Adv. Math., Vol. 74, Cambridge University Press, Cambridge 2002.
  • [10] I. Fahrner and U. Stadtmüller, On almost sure max-limit theorems, Statist. Probab. Lett. 37 (1998), pp. 229-236.
  • [11] A. Fisher, A pathwise central limit theorem for random walks, preprint, 1989.
  • [12] J. Galambos, The Asymptotic Theory of Extreme Order Statistics, Wiley Ser. Probab. Math. Statist., New York-Chichester-Brisbane 1978.
  • [13] S. Hörmann, An extension of the almost sure central limit theorem, Statist. Probab. Lett. 76 (2006), pp. 191-202.
  • [14] S. Hörmann, Critical behavior in almost sure central limit theory, preprint.
  • [15] I. A. Ibragimov and M. A. Lifshits, On limit theorems of "almost sure" type, Theory Probab. Appl. 44 (2000), pp. 254-272.
  • [16] M. T. Lacey and W. Philipp, A note on the almost sure central limit theorem, Statist. Probab. Lett. 9 (1990), pp. 201-205.
  • [17] E. Lesigne, Almost sure central limit theorem for strictly stationary processes, Roc. Amer. Math. Soc. 128 (2000), pp. 1751-1759.
  • [18] L. Peng and Y. Qi, Almost sure convergence of the distributional limit theorem for order statistics, Probab. Math. Statist. 23 (2003), pp. 217-228.
  • [19] R.-D. Reiss, Approximate Distributions of Order Statistics, Springer, New York 1989.
  • [20] Y. A. Rozanov, Stationary Random Processes, Holden-Day, 1967.
  • [21] P. Schatte, On strong versions of the central limit theorem, Math. Nachr. 137 (1988), pp. 249-256.
  • [22] U. Stadtmüller, Almost sure versions of distributional limit theorems for certain order statistics, Statist. Probab. Lett. 58 (2002), pp. 413-426.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a8b227ed-5e35-4bce-93c2-e55b6aecddf5
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