On the law of iterated logarithm for occupation measures of empirical processes

Gutti Jogesh Babu

doi:10.1007/BF00534995

On the law of iterated logarithm for occupation measures of empirical processes

Gutti Jogesh Babu

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Abstract

Let {K(s,t): 0≦s≦1, t≧0} be a Kiefer process. Let {Mathematical expression} denote the occupation distribution. Using the ideas of Mogul'skii, Donsker and Varadhan, the limit behavior of L_t is studied. These and strong approximation results are then used to derive LIL in Chung's form for various functions of empirical processes.

Original language	English (US)
Pages (from-to)	73-81
Number of pages	9
Journal	Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume	65
Issue number	1
DOIs	https://doi.org/10.1007/BF00534995
State	Published - Mar 1983

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
General Mathematics

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abstract = "Let \{K(s,t): 0≦s≦1, t≧0\} be a Kiefer process. Let \{Mathematical expression\} denote the occupation distribution. Using the ideas of Mogul'skii, Donsker and Varadhan, the limit behavior of Lt is studied. These and strong approximation results are then used to derive LIL in Chung's form for various functions of empirical processes.",

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N2 - Let {K(s,t): 0≦s≦1, t≧0} be a Kiefer process. Let {Mathematical expression} denote the occupation distribution. Using the ideas of Mogul'skii, Donsker and Varadhan, the limit behavior of Lt is studied. These and strong approximation results are then used to derive LIL in Chung's form for various functions of empirical processes.

AB - Let {K(s,t): 0≦s≦1, t≧0} be a Kiefer process. Let {Mathematical expression} denote the occupation distribution. Using the ideas of Mogul'skii, Donsker and Varadhan, the limit behavior of Lt is studied. These and strong approximation results are then used to derive LIL in Chung's form for various functions of empirical processes.

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ER -

On the law of iterated logarithm for occupation measures of empirical processes

Abstract

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