Abstract
Let {X n ; n ≥ 1} be a sequence of independent and identically distributed random vectors in ℜp with Euclidean norm |·|, and let X (r) n = 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 (1) n + ... + X (r) n ). In this paper a generalized strong invariance principle for the trimmed sums (r) S n is derived.
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Fu, KA. An almost sure invariance principle for trimmed sums of random vectors. Proc Math Sci 120, 611–618 (2010). https://doi.org/10.1007/s12044-010-0052-x
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DOI: https://doi.org/10.1007/s12044-010-0052-x