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- Title
A nonclassical LIL for sums of B-valued random variables when extreme terms are excluded.
- Authors
Fu, Ke-Ang
- Abstract
Let { X, X; n≧1} be a sequence of B-valued i.i.d. random variables. Denote $X_{{n}}^{(r)}=X_{{m}}$ if ∥ X∥ is the r-th maximum of {∥ X∥; k≦ n}, and let ${}^{(r)}S_{{n}}=S_{{n}}-(X_{{n}}^{(1)}+\cdots+X_{{n}}^{(r)})$ be the trimmed sums, where $S_{{n}}=\sum_{ k=1}^{n}X_{{k}}$. Given a sequence of positive constants { h( n), n≧1}, which is monotonically approaching infinity and not asymptotically equivalent to loglog n, a limit result for $^{(r)}S_{{n}}/\sqrt{2nh(n)}$ is derived.
- Subjects
NONCLASSICAL mathematical logic; NUMERICAL solutions to boundary value problems; RANDOM variables; MATHEMATICAL sequences; MATHEMATICAL constants; BANACH spaces; ITERATIVE methods (Mathematics)
- Publication
Acta Mathematica Hungarica, 2012, Vol 137, Issue 1/2, p1
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1007/s10474-012-0209-4