The almost sure behavior of maximal and minimal multivariate \(k_ n\)- spacings
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Publication:1103953
DOI10.1016/0047-259X(88)90109-1zbMath0646.60035OpenAlexW2097673396MaRDI QIDQ1103953
David M. Mason, John H. J. Einmahl, Paul Deheuvels, Frits H. Ruymgaart
Publication date: 1988
Published in: Journal of Multivariate Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0047-259x(88)90109-1
entropy conditionsstrong lawsincrements of the empirical measuresiterated-logarithm type lawmaximal k-spacingsminimal k-spacingsmultivariate k-spacings
Related Items (12)
Nonstandard local empirical processes indexed by sets ⋮ Sharp tail distribution estimates for the supremum of a class of sums of i.i.d. random variables ⋮ Random Euclidean coverage from within ⋮ Some limit theorems for the homogeneous Poisson process ⋮ Limit theorems for the minimum interpoint distance between any pair of i.i.d. random points in \(R^ d\) ⋮ On the Hausdorff dimension of exceptional random sets generated by multivariate spacings ⋮ Inner rates of coverage of Strassen type sets by increments of the uniform empirical and quantile processes ⋮ Nonparametric likelihood based estimation for a multivariate Lipschitz density ⋮ Gaussian limits for generalized spacings ⋮ Limit theorems for the negative parts of weighted multivariate empirical processes with application ⋮ Functional laws of the iterated logarithm for small increments of empirical processes ⋮ On the number of points of a homogeneous Poisson process
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- Strong bounds for weighted empirical distribution functions based on uniform spacings
- Laws of the iterated logarithm for order statistics of uniform spacings
- A log log law for maximal uniform spacings
- Strong limiting bounds for maximal uniform spacings
- Strong laws for the maximal k-spacing when k?c log n
- Upper and lower class sequences for minimal uniform spacings
- Entropy and maximal spacings for random partitions
- Strong bounds for multidimensional spacings
- An inequality involving multinomial probabilities
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