An almost sure invariance principle for trimmed sums of random vectors

作者：Fu, Ke-Ang^*

来源：Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2010, 120(5): 611-618.

DOI：10.1007/s12044-010-0052-x

• Trimmed sums
• strong invariance principle
• law of the iterated logarithm

Let {X(n); n >= 1} be a sequence of independent and identically distributed random vectors in R(p) with Euclidean norm vertical bar . vertical bar, and let X(n)((r)) = X(m) if vertical bar X(m)vertical bar is the r-th maximum of {vertical bar X(k)vertical bar; k <= n}. Define S(n) = Sigma(k <= n) X(k) and ((r))S(n) = S(n) - (X(n)((1)) + ... + X(n)((r))). In this paper a generalized strong invariance principle for the trimmed sums ((r))S(n) is derived.

• 出版日期2010-11
• 单位浙江工商大学