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The moderate deviation principle for self-normalized sums of sums of i.i.d. random variables

✍ Scribed by Bin Qian; Jun Yan

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
326 KB
Volume
22
Category
Article
ISSN
0893-9659

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✦ Synopsis

The corresponding moderate deviation principle follows. The Central Limit theorem has been recently obtained by Pang, Lin and Hwang [T.X. Pang, Z.Y. Lin, K.S. Hwang, Asymptotics for self-normalized random products of sums of i.i.d. random variables, J. Math. Anal. Appl. 334 (2007) 1246-1259].

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is non-decreasing. Thus, if one applies the c,-inequality, the inequality follows trivially. From this and from the preceding inequality we obtain By our condition the sums on the right hand side converge to 0 as n -+ + 00. This proves the assertion. Remarks. It is easy to see that for p > 2 our c