Optimal averaging procedures in almost sure central limit theory

Povzetek

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.

Ključne besede

Statistične metode;

Podatki

Jezik:	Angleški jezik
Leto izida:	2005
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FDV - Fakulteta za družbene vede
Založnik:	Fakulteta za družbene vede
UDK:	311
COBISS:	24318301
ISSN:	1854-0023
Št. ogledov:	160
Št. prenosov:	32
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Neznan jezik
Sekundarne ključne besede:	Statistical methods;
URN:	URN:NBN:SI
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	str. 271-282
Letnik:	ǂVol. ǂ2
Zvezek:	ǂno. ǂ2
Čas izdaje:	2005
Ključne besede (UDK):	social sciences;družbene vede;statistics as a science;statistical theory;statistika;statistična teorija;
ID:	1467973