TY - JOUR
T1 - Some bounds on the rate of convergence in the CLT for martingales. I
AU - Rinott, Y.
AU - Rotar, V.
PY - 1998/12
Y1 - 1998/12
N2 - This paper concerns rates of convergence in the central limit theorem (CLT) for the random variables Sn = ∑n1 Xm, where Xm are martingale-differences. It is known that in the general case one cannot hope for a rate better than O(n-1/8) even if the third moments are finite. If the conditional variances satisfy E{X2m, | X1i , . . . , Xm-1} = EX2m, the rate in general is no better than O(n-1/4}, while in the independency case it is of the order O(n-1/2). This paper contains a bound which covers simultaneously the cases mentioned as well as some intermediate cases. The bound is presented in terms of some dependency characteristics reflecting the influence of different factors on the rate.
AB - This paper concerns rates of convergence in the central limit theorem (CLT) for the random variables Sn = ∑n1 Xm, where Xm are martingale-differences. It is known that in the general case one cannot hope for a rate better than O(n-1/8) even if the third moments are finite. If the conditional variances satisfy E{X2m, | X1i , . . . , Xm-1} = EX2m, the rate in general is no better than O(n-1/4}, while in the independency case it is of the order O(n-1/2). This paper contains a bound which covers simultaneously the cases mentioned as well as some intermediate cases. The bound is presented in terms of some dependency characteristics reflecting the influence of different factors on the rate.
KW - Central limit theorem
KW - Martingales
KW - Rate of convergence
UR - http://www.scopus.com/inward/record.url?scp=0032223447&partnerID=8YFLogxK
U2 - 10.1137/s0040585x97977148
DO - 10.1137/s0040585x97977148
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0032223447
SN - 0040-585X
VL - 43
SP - 604
EP - 619
JO - Theory of Probability and its Applications
JF - Theory of Probability and its Applications
IS - 4
ER -