Limit laws of modulus trimmed sums

• 成果类型: Article
• 署名作者: Griffin, PS; Qazi, FS
• 署名单位: Syracuse University; St. Marys College of Maryland
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2002
• 页码: 1466-1485
• 关键词: Asymptotic Normality

摘要

Let X, X-1, X-2,... be a sequence of independent and identically distributed random variables. Let X-(1)(n),...,X-(n)(n) be an arrangement of X-1, X-2,..., X-n in decreasing order of magnitude, and set((rn))S(n) = X-(rn+1)(n) + (...) + X-(n)(n). This is known as the modulus trimmed sum. We obtain a complete characterization of the class of limit laws of the normalized modulus trimmed sum when the underlying distribution is symmetric and r(n) --> infinity, r(n)n(-1) --> 0.