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.
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
18
号
4
ページ
397 - 427
発行年
2012-03-30
ISSN
13405705
書誌レコードID
AA11021653
日本十進分類法
415
Mathematical Reviews Number
MR
Mathmatical Subject Classification
60F05(MSC2010)
62E20(MSC2010)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
原稿受領日
2010-12-25
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Uniform Estimates for Distributions of the Sum of i.i.d. Random Variables with Fat Tail in the Threshold Case
jms180401.pdf
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