35 KB116 KB24 KB200420242005Hörmann, Siegfried12 straništevilka:2letnik:2str. 271-282ISSN:1854-0023ISSN:1854-0031COBISSID:24318301URN:URN:NBN:SI:doc-VYBQJE9ZenFakulteta za družbene vedeMetodološki zvezkimatematična statistikaStatistical methodsStatistične metodestohastični procesiOptimal averaging procedures in almost sure central limit theory|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/!Ik !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 holdTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza v Ljubljani, Fakulteta za družbene vede