Deheuvels, Paul; Devroye, Luc Strong laws for the maximal k-spacing when k\(\leq c \log n\). (English) Zbl 0525.60035 Z. Wahrscheinlichkeitstheor. Verw. Geb. 66, 315-334 (1984). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 Documents MSC: 60F15 Strong limit theorems 60F10 Large deviations 62G30 Order statistics; empirical distribution functions Keywords:spacings; order statistics; laws of the iterated logarithm; Erdős- Renyi theorem; oscillation modulus; uniform empirical quantile process; density estimation; partial sums PDFBibTeX XMLCite \textit{P. Deheuvels} and \textit{L. Devroye}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 66, 315--334 (1984; Zbl 0525.60035) Full Text: DOI References: [1] Barndorff-Nielsen, O., On the rate of growth of the partial maxima of a sequence of independent identically distributed random variables, Math. Scand., 9, 383-394 (1961) · Zbl 0209.20104 [2] Deheuvels, P., Strong limiting bounds for maximal uniform spacings, Ann. Probability, 10, 1058-1065 (1982) · Zbl 0505.60033 · doi:10.1214/aop/1176993728 [3] Deheuvels, P., Devroye, L.: Limit laws related to the Erdös-Rényi theorem. Submitted (1983) · Zbl 0637.60039 [4] Del Pino, G. E., On the asymptotic distribution of k-spacings with applications to goodness-of-fit tests, Ann. Statist., 7, 1058-1065 (1979) · Zbl 0425.62026 · doi:10.1214/aos/1176344789 [5] Devroye, L., Laws of the iterated logarithm for order statistics of uniform spacings, Ann. Probability, 9, 860-867 (1981) · Zbl 0465.60038 · doi:10.1214/aop/1176994313 [6] Devroye, L., A log log law for maximal uniform spacings, Ann. Probability, 10, 863-868 (1982) · Zbl 0491.60030 · doi:10.1214/aop/1176993799 [7] Erdös, P.; Rényi, A., On a new law of large numbers, J. Analyse Math., 23, 103-111 (1970) · Zbl 0225.60015 · doi:10.1007/BF02795493 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.