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The Law of the Iterated Logarithm for a Triangular Array of Empirical Processes

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1.	Title	Title of document	The Law of the Iterated Logarithm for a Triangular Array of Empirical Processes
2.	Creator	Author's name, affiliation, country	Miguel A. Arcones; State University of New York
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	Empirical process, law of the iterated logarithm, triangular array, density estimation.
3.	Subject	Subject classification	60B12, 60F15
4.	Description	Abstract	We study the compact law of the iterated logarithm for a certain type of triangular arrays of empirical processes, appearing in statistics (M-estimators, regression, density estimation, etc). We give necessary and sufficient conditions for the law of the iterated logarithm of these processes of the type of conditions used in Ledoux and Talagrand (1991): convergence in probability, tail conditions and total boundedness of the parameter space with respect to certain pseudometric. As an application, we consider the law of the iterated logarithm for a class of density estimators. We obtain the order of the optimal window for the law of the iterated logarithm of density estimators. We also consider the compact law of the iterated logarithm for kernel density estimators when they have large deviations similar to those of a Poisson process.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1997-08-18
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/19
10.	Identifier	Digital Object Identifier	10.1214/EJP.v2-19
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 2
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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