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  • Optimal averaging procedures in almost sure central limit theory
    Hörmann, Siegfried
    Let X1,X2, . . . be i.i.d. random variables with EX1 = 0,EX2 1 = 1, Sn = X1 +.. .+Xn and let (dk) be a positive numerical sequence. We investigate the a.s. convergence of the averages 1 DN N Xk=1 ... dkI{Sk/¡Ìk ¡Ü x} ,where DN = PN k=1 dk. In the case of dk = 1/k we have logarithmic means and by the almost sure central limit theorem the above averages converge a.s. (x), the standard normal distribution function. It is also known that the analogous convergence relation fails for dk = 1 (ordinary averages). In this paper we give a fairly complete solution of the problem for which weight sequences the above convergence relation and its refinements hold.
    Vir: Advances in methodology and statistics = Metodološki zvezki. - ISSN 1854-0023 (Vol. 2, no. 2, 2005, str. 271-282)
    Vrsta gradiva - članek, sestavni del
    Leto - 2005
    Jezik - angleški
    COBISS.SI-ID - 24318301

    Povezava(-e):

    http://mrvar.fdv.uni-lj.si/pub/mz/mz2.1/hoerman.pdf
    Digitalna knjižnica Slovenije - dLib.si
    Repozitorij Univerze v Ljubljani – RUL

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