An almost sure invariance principle for trimmed sums of random vectors |
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Authors: | Ke-Ang Fu |
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Affiliation: | (1) Departement Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium |
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Abstract: | Let {X n ; n ≥ 1} be a sequence of independent and identically distributed random vectors in ℜ p with Euclidean norm |·|, and let X n (r) = X m if |X m | is the r-th maximum of {|X k |; k ≤ n}. Define S n = Σ k≤n X k and (r) 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. |
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