Abstract
In this paper, we extend the Hölderian invariance principle of Lamperti [6] to the case of partial-sum processes based on a triangular array of row-wise independent random variables. As an application, we obtain necessary and sufficient conditions for the almost sure (resp. in probability) weak Hölder convergence of partial-sum processes based on bootstrapped samples.
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Račkauskas, A., Suquet, C. Hölderian Invariance Principle for Triangular Arrays of Random Variables. Lithuanian Mathematical Journal 43, 423–438 (2003). https://doi.org/10.1023/B:LIMA.0000009690.57986.d1
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DOI: https://doi.org/10.1023/B:LIMA.0000009690.57986.d1