본문 바로가기
KERD
논문KCI 등재

A self-normalized LIL for conditionally trimmed sums and conditionally censored sums

Tian-xiao Pang|Zheng-yan Lin
대한수학회 (The Korean Mathematical Society)|2006.07|대한수학회지 (Journal of the KMS)|제43권 제4호|pp. 859-869

0

조회

0

다운로드

0

인용

0

참고문헌

주제분류수학

초록

Abstract

Let {X, X_n; nge 1} be a sequence of i.i.d. randomvariables which belong to the attraction of the normal law, andX_n^{(1)}, ldots, X_n^{(n)} be an arrangement of X_1, ldots,X_n in decreasing order of magnitude, i.e., |X_n^{(1)}|gecdots ge |X_n^{(n)}|. Suppose that {r_n} is a sequence ofconstants satisfying some mild conditions and d^{'}(t_{n_k}) isan appropriate truncation level, where n_k=[beta^k] and betais any constant larger than one. Then we show that theconditionally trimmed sums obeys the self-normalized law of theiterated logarithm (LIL). Moreover, the self-normalized LIL for

참고문헌 (13)

  1. "The Berry-Esseen boundfor Student's statistic", 24(1), pp.491~503 (1996)
  2. "Studentizedincrements of partial sums", pp.265~ (1994)
  3. "Donsker's theorem for self-nor-malized partial sumsprocesses", 31(3), pp.1228~1240 (2003)
  4. "An Introduction to Probability and ItsApplications. Vol. I" (1968), Inc.
  5. "When is theStudent t-statistic asymptotically standard normal?", 25(3), pp.1514~1531 (1997)
  6. "Non-classical law of the iteratedlogarithm behaviour for trimmed sums", 78(2), pp.293~ (1988)
  7. "Self-normalized laws ofthe iterated logarithm", 17(4), pp.1571~ (1989)
  8. "Universal asymptotic normality forconditionally trimmed sums", 7(1), pp.9~ (1988)
  9. "A universal law of the iterated logarithm for trimmed andcensored sums Lecture Notes in Math. 1391" (1989)
  10. "The law of the iterated logarithmfor the rescaled R", S statistics without the second moment, 2004, pp.47(8-9), 1389~1396
  11. "A self-normalized Chung type lawof the iterated logarithm", 41(4), pp.791~798 (1996)
  12. "Limit theorems on the self-normalizedrange for weakly and strongly dependent processes", 31, pp.271~ (1975)
  13. "Recent developments on self-normalizedlimit theorems. In Asymptotic methods in probability andstatistics", pp.467~480 (1998)

관련 논문AI추천

Limit theorems for partial sum processes of a Gaussian sequence백종일, 최용갑, Hee-Jin Moon, Kyo-Shin Hwang, Tae-Sung Kim대한수학회 · 대한수학회지2004 · 제41권 제6호Limsup results and a generalized uniform LIL for an LPQD sequence문희진, 최용갑, 황교신대한수학회 · 대한수학회지2012 · 제49권 제2호Limit theorems for partial sum processes of a Gaussian SequenceYong-Kab Choi, Kyo-Shin Hwang, Hee-Jin Moon, Tae-S대한수학회 · 대한수학회지2004 · 제41권 제6호Limsup Results and Lil for Partial Sums of Random Sequences문희진, 최용갑, 한창호영남수학회 · East Asian Mathematical Journal2014 · 제30권 제1호SELF-NORMALIZED WEAK LIMIT THEOREMS FOR A φ-MIXING SEQUENCE문희진, 최용갑대한수학회 · 대한수학회보2010 · 제47권 제6호Strassen's functional LIL for $d$-dimensional self-similar Gaussian process in H\＂older norm황교신, Zhengyan Lin대한수학회 · 대한수학회지2005 · 제42권 제5호

이 간행물의 다른 논문 (13건)

Exotic smooth structure on $\Bbb {CP}^2\sharp 13 \overline {\Bbb {CP}}^2$홍윤희, 조용승pp. 691-701The operational calculus for a measure-valued Dyson series류근식pp. 703-715Slant Submanifolds of an Almost Product Riemannian ManifoldBayram Sahinpp. 717-732Existence of quasi-stationary Stokes flow in a dihedral domain진범자pp. 733-763Stable vector bundles of rank two on Enriques surfaces김호일pp. 765-782
원문 보기