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Quantile coupling inequalities and their applications. (English) Zbl 1307.62036

Summary: This is partly an expository paper. We prove and highlight a quantile inequality that is implicit in the fundamental paper by J. Komlós et al. [Z. Wahrscheinlichkeitstheor. Verw. Geb. 32, 111–131 (1975; Zbl 0308.60029)] on Brownian motion strong approximations to partial sums of independent and identically distributed random variables. We also derive a number of refinements of this inequality, which hold when more assumptions are added. A number of examples are detailed that will likely be of separate interest. We especially call attention to applications to the asymptotic equivalence theory of nonparametric statistical models and nonparametric function estimation.

MSC:

62E17 Approximations to statistical distributions (nonasymptotic)
62B15 Theory of statistical experiments
62G05 Nonparametric estimation

Citations:

Zbl 0308.60029
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Full Text: DOI Euclid

References:

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