Two-parameter strong laws and maximal inequalities for U-statistics

Terry R. McConnell

doi:10.1017/S0308210500029401

Two-parameter strong laws and maximal inequalities for U-statistics

Terry R. McConnell

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We provide necessary and sufficient conditions for two-parameter convergence in the strong law of large numbers for U-statistics. We also obtain weak-type (1,1) inequalities for one and two-sample U-statistics of order 2 which are, in a sense, best possible.

Original language	English (US)
Pages (from-to)	133-151
Number of pages	19
Journal	Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume	107
Issue number	1-2
DOIs	https://doi.org/10.1017/S0308210500029401
State	Published - 1987

ASJC Scopus subject areas

General Mathematics

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title = "Two-parameter strong laws and maximal inequalities for U-statistics",

abstract = "We provide necessary and sufficient conditions for two-parameter convergence in the strong law of large numbers for U-statistics. We also obtain weak-type (1,1) inequalities for one and two-sample U-statistics of order 2 which are, in a sense, best possible.",

author = "McConnell, {Terry R.}",

note = "Funding Information: * Supported in part by NSF Grant DMS 85-03775 and by the Alfred P. Sloan Foundation.",

year = "1987",

doi = "10.1017/S0308210500029401",

language = "English (US)",

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pages = "133--151",

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publisher = "Cambridge University Press",

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AU - McConnell, Terry R.

N1 - Funding Information: * Supported in part by NSF Grant DMS 85-03775 and by the Alfred P. Sloan Foundation.

PY - 1987

Y1 - 1987

N2 - We provide necessary and sufficient conditions for two-parameter convergence in the strong law of large numbers for U-statistics. We also obtain weak-type (1,1) inequalities for one and two-sample U-statistics of order 2 which are, in a sense, best possible.

AB - We provide necessary and sufficient conditions for two-parameter convergence in the strong law of large numbers for U-statistics. We also obtain weak-type (1,1) inequalities for one and two-sample U-statistics of order 2 which are, in a sense, best possible.

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U2 - 10.1017/S0308210500029401

DO - 10.1017/S0308210500029401

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JO - Proceedings of the Royal Society of Edinburgh: Section A Mathematics

JF - Proceedings of the Royal Society of Edinburgh: Section A Mathematics

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Two-parameter strong laws and maximal inequalities for U-statistics

Abstract

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