caa a22 4500 606244700 CHVBK 20210128101331.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s12044-015-0224-9 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0224-9 Limit law of the iterated logarithm for B -valued trimmed sums [Elektronische Daten] [KE-ANG FU, YUYANG QIU, YELING TONG] Given a sequence of i.i.d. random variables {X,X n ;n≥1} taking values in a separable Banach space (B, ∥⋅∥) with topological dual B ∗, let X n ( r ) = X m $X_{n}^{(r)}=X_{m}$ if ∥X m ∥ is the r-th maximum of {∥X k ∥;1≤k≤n} and ( r ) S n = S n − ( X n ( 1 ) + ⋯ + X n ( r ) ) ${}^{(r)}S_{n}=S_{n}-(X_{n}^{(1)}+\cdots +X_{n}^{(r)})$ be the trimmed sums when extreme terms are excluded, where S n = ∑ k = 1 n X k $S_{n}={\sum }_{k=1}^{n}X_{k}$ . In this paper, it is stated that under some suitable conditions, lim n → ∞ 1 2 log log n max 1 ≤ k ≤ n ∥ ( r ) S k ∥ k = σ ( X ) a . s . , $\lim _{n\to \infty }\frac {1}{\sqrt {2\log \log n}}\max _{1\le k\le n}\frac {\|^{(r)}S_{k}\|}{\sqrt {k}}=\sigma (X)~~~\mathrm {a.s.},$ where σ 2 ( X ) = sup f ∈ B 1 ∗ E f 2 ( X ) $\sigma ^{2}(X)=\sup _{f\in B_{1}^{*}}\text {\textsf {E}} f^{2}(X)$ and B 1 ∗ $B_{1}^{*}$ is the unit ball of B ∗. Indian Academy of Sciences, 2015 Banach space nationallicence trimmed sums nationallicence the limit law of the iterated logarithm nationallicence FU KE-ANG School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, China aut QIU YUYANG School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, China aut TONG YELING Zhejiang Institute of Traditional Chinese Medicine, 310028, Hangzhou, China aut Proceedings - Mathematical Sciences Springer India 125/2(2015-05-01), 221-225 0253-4142 125:2<221 2015 125 12044 https://doi.org/10.1007/s12044-015-0224-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s12044-015-0224-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- FU KE-ANG School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, China aut NATIONALLICENCE 700 1- QIU YUYANG School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, China aut NATIONALLICENCE 700 1- TONG YELING Zhejiang Institute of Traditional Chinese Medicine, 310028, Hangzhou, China aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/2(2015-05-01), 221-225 0253-4142 125:2<221 2015 125 12044