Optimal averaging procedures in almost sure central limit theory

Abstract

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.

Keywords

Statistične metode;

Data

Language:	English
Year of publishing:	2005
Typology:	1.01 - Original Scientific Article
Organization:	UL FDV - Faculty of Social Sciences
Publisher:	Fakulteta za družbene vede
UDC:	311
COBISS:	24318301
ISSN:	1854-0023
Views:	160
Downloads:	32
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Unknown
Secondary keywords:	Statistical methods;
URN:	URN:NBN:SI
Type (COBISS):	Not categorized
Pages:	str. 271-282
Volume:	ǂVol. ǂ2
Issue:	ǂno. ǂ2
Chronology:	2005
Keywords (UDC):	social sciences;družbene vede;statistics as a science;statistical theory;statistika;statistična teorija;
ID:	1467973