TY - JOUR
T1 - On normal approximation rates for certain sums of dependent random variables
AU - Rinott, Yosef
PY - 1994/11/21
Y1 - 1994/11/21
N2 - Let X1, ..., Xn be dependent random variables, and set λ = E∑ni=1Xi, and σ2 = Var∑ni=1Xi. In most of the applications of Stein's method for normal approximations, the error rate |P((∑ni=1Xi - λ)/σ ≤ w) - Φ(w)| is of the order of σ- 1 2. This rate was improved by Stein (1986) and others in some special cases. In this paper it is shown that for certain bounded random variables, a simple refinement of error-term calculations in Stein's method leads to improved rates.
AB - Let X1, ..., Xn be dependent random variables, and set λ = E∑ni=1Xi, and σ2 = Var∑ni=1Xi. In most of the applications of Stein's method for normal approximations, the error rate |P((∑ni=1Xi - λ)/σ ≤ w) - Φ(w)| is of the order of σ- 1 2. This rate was improved by Stein (1986) and others in some special cases. In this paper it is shown that for certain bounded random variables, a simple refinement of error-term calculations in Stein's method leads to improved rates.
KW - Central limit theorem
KW - Dependency graph
KW - Stein's method
UR - http://www.scopus.com/inward/record.url?scp=0000060362&partnerID=8YFLogxK
U2 - 10.1016/0377-0427(94)90016-7
DO - 10.1016/0377-0427(94)90016-7
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0000060362
SN - 0377-0427
VL - 55
SP - 135
EP - 143
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 2
ER -