SLOW CONVERGENCE TO NORMALITY:
AN EDGEWORTH EXPANSION WITHOUT THIRD MOMENT
Abstract: Let
be a non-lattice distribution function which lies in the domain of attraction
of a normal distribution. Exact uniform convergence rates are obtained for the convergence of
the normalized partial sums of i.i.d. random variables with distribution
The assumptions
are
![1- F(x)+ F (-x) (- RV (- 1 < r < 0)
r-2](files/17.2/HTML/17.2.12.abs2x.png)
and
![(1- F (x))/(1- F (x) + F(-x))-- > p (- [0,1] (as x-- > oo ).](files/17.2/HTML/17.2.12.abs3x.png)
For
![r = -1](files/17.2/HTML/17.2.12.abs4x.png)
somewhat weaker conditions are sufficient.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -