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Strong laws for the maximal k-spacing when k\(\leq c \log n\). (English) Zbl 0525.60035


MSC:

60F15 Strong limit theorems
60F10 Large deviations
62G30 Order statistics; empirical distribution functions
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References:

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[3] Deheuvels, P., Devroye, L.: Limit laws related to the Erdös-Rényi theorem. Submitted (1983) · Zbl 0637.60039
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[8] Hall, P., Laws of the iterated logarithm for nonparametric density estimators, Zeitschrift für Wahrscheinlichkeitstheorie verw. Gebiete, 56, 47-61 (1981) · Zbl 0443.62027 · doi:10.1007/BF00531973
[9] Mason, D. M., A strong limit theorem for the oscillation modulus of the uniform empirical quantile process, Stochastic Processes and their Applications, 17, 127-136 (1984) · Zbl 0531.60035 · doi:10.1016/0304-4149(84)90315-6
[10] Révész, P., On the increments of Wiener and related processes, Ann. Probability, 10, 613-622 (1982) · Zbl 0493.60038 · doi:10.1214/aop/1176993771
[11] Stute, W., The oscillation behavior of empirical processes, Ann. Probability, 10, 86-107 (1982) · Zbl 0489.60038 · doi:10.1214/aop/1176993915
[12] Stute, W., A law of the logarithm for kernel density estimators, Ann. Probability, 10, 414-422 (1982) · Zbl 0493.62040 · doi:10.1214/aop/1176993866
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