Strong laws for the maximal k-spacing when k?c log n

DOI10.1007/BF00533700zbMath0525.60035MaRDI QIDQ3038292

Paul Deheuvels, Luc P. Devroye

Publication date: 1984

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

zbMATH Keywords

order statisticsspacingspartial sumsdensity estimationlaws of the iterated logarithmuniform empirical quantile processoscillation modulusErdős- Renyi theorem

Mathematics Subject Classification ID

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

Related Items (9)

The almost sure behavior of maximal and minimal multivariate \(k_ n\)- spacings ⋮ Optimal rules for the sequential selection of uniform spacings ⋮ Uniform-in-bandwidth nearest-neighbor density estimation ⋮ Functional laws of the iterated logarithm for large increments of empirical and quantile processes ⋮ Nonstandard strong laws for local quantile processes ⋮ Unnamed Item ⋮ On the weak limit law of the maximal uniform k-spacing ⋮ Functional laws of the iterated logarithm for small increments of empirical processes ⋮ Strong laws for the k-th order statistic when k\(\leq c\,\log _ 2\,n\)

Cites Work

• A strong limit theorem for the oscillation modulus of the uniform empirical quantile process
• Limit laws of Erdős-Rényi-Shepp type
• On the asymptotic distribution of k-spacings with applications to goodness-of-fit tests
• Laws of the iterated logarithm for order statistics of uniform spacings
• The oscillation behavior of empirical processes
• A log log law for maximal uniform spacings
• On the increments of Wiener and related processes
• A law of the logarithm for kernel density estimators
• Strong limiting bounds for maximal uniform spacings
• On a new law of large numbers
• Laws of the iterated logarithm for nonparametric density estimators
• On the Rate of Growth of the Partial Maxima of a Sequence of Independent Identically Distributed Random Variables.

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