id: 05519518
dt: j
an: 2012a.00670
au: Goldstein, Larry
ti: A probabilistic proof of the Lindeberg-Feller central limit theorem.
so: Am. Math. Mon. 116, No. 1, 45-60 (2009).
py: 2009
pu: Mathematical Association of America (MAA), Washington, DC
la: EN
cc: K55
ut: Lindeberg-Feller central limit theorem; probabilistic proof; Stein’s
characterization of normal distribution; zero bias transformation
ci:
li: doi:10.4169/193009709X469788
ab: The author presents a simple and easily interpretable probabilistic
formulation of the Lindeberg condition and demonstrates its sufficiency
and partial necessity in the Central Limit Theorem (CTL) using
elementary means. The proof is based on the so-called zero bias
transformation, which is motivated by Stein’s characterization of the
mean zero normal distribution with variance $σ^2$.
rv: Wiesław Dziubdziela (Kielce)