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Maxima of the cells of an equiprobable multinomial

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Maxima of the cells of an equiprobable multinomial
2.	Creator	Author's name, affiliation, country	Arup Bose; Indian Statistical Institute
2.	Creator	Author's name, affiliation, country	Amites Dasgupta; Indian Statistical Institute
2.	Creator	Author's name, affiliation, country	Krishanu Maulik; Indian Statistical Institute
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Random sequences; triangular array; maxima; limit distribution
3.	Subject	Subject classification	Primary 60G70, 60F05; Secondary 60F10
4.	Description	Abstract	Consider a sequence of multinomial random vectors with increasing number of equiprobable cells. We show that if the number of trials increases fast enough, the sequence of maxima of the cells after a suitable centering and scaling converges to the Gumbel distribution. While results are available for maxima of triangular arrays of independent random variables with certain types of distribution, such results in a dependent setup is new. We also prove that the maxima of a triangular sequence of appropriate Binomial random variables have the same limit distribution. An auxiliary large deviation result for multinomial distribution with increasing number of equiprobable cells may also be of independent interest.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2007-04-24
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1260
10.	Identifier	Digital Object Identifier	10.1214/ECP.v12-1260
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 12
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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