 On the law of the iterated logarithm for canonical U-statistics and processesMiguel A. Arcones and Evarist Giné Stochastic Processes and their Applications, 1995, vol. 58, issue 2, 217-245 Abstract: The law of the iterated logarithm for canonical or completely degenerate U-statistics with square integrable kernel h is proved, for h taking values in 1, 7 and, in general, in a type 2 separable Banach space. The LIL is also obtained for U-processes indexed by canonical Vapnik-Cervonenkis classes of functions with square integrable envelope and, in this regard, an equicontinuity condition equivalent to the LIL property is quite helpful. Some of these results are then applied to obtain the a.s. exact order of the remainder term in the linearization of the product limit estimator for truncated data; a consequence for density estimation is also included. Keywords: Law; of; the; iterated; logarithm; Canonical; (or; completely; degenerate); U-statistics; Canonical; U-processes; Product; limit; estimator; Truncated; data; Density; estimation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:58:y:1995:i:2:p:217-245 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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