Uniform Estimates for Distributions of the Sum of i.i.d. Random Variables with Fat Tail in the Threshold Case

J. Math. Sci. Univ. Tokyo
Vol. 18 (2011), No. 4, Page 397--427.

Nakahara, Kenji
Uniform Estimates for Distributions of the Sum of i.i.d. Random Variables with Fat Tail in the Threshold Case
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]


Abstract:
We show uniform estimates for distributions of the sum of i.i.d. random variables in the threshold case. Rozovskii showed several uniform estimates but the speed of convergence was not known. Our main uniform estimate implies a speed of convergence. We also compare our estimates with Nagaev's estimate which is valid in the non-threshold case and, moreover, give a necessary and sufficient condition for Nagaev's estimate to hold in the threshold case.

Mathematics Subject Classification (2010): Primary 60F05, Secondary 62E20.
Received: 2010-12-25