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Limit Theorems for the Number of Maxima in Random Samples from Planar Regions


 
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1. Title Title of document Limit Theorems for the Number of Maxima in Random Samples from Planar Regions
 
2. Creator Author's name, affiliation, country Zhi-Dong Bai; National University of Singapore
 
2. Creator Author's name, affiliation, country Hsien-Kuei Hwang; Academia Sinica
 
2. Creator Author's name, affiliation, country Wen-Qi Liang; Academia Sinica
 
2. Creator Author's name, affiliation, country Tsung-Hsi Tsai; Academia Sinica
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Maximal points, multicriterial optimization, central limit theorems, Poisson approximations, convex polygons.
 
3. Subject Subject classification Primary. 60D05; Secondary. 60C05
 
4. Description Abstract We prove that the number of maximal points in a random sample taken uniformly and independently from a convex polygon is asymptotically normal in the sense of convergence in distribution. Many new results for other planar regions are also derived. In particular, precise Poisson approximation results are given for the number of maxima in regions bounded above by a nondecreasing curve.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2001-01-22
 
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/76
 
10. Identifier Digital Object Identifier 10.1214/EJP.v6-76
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 6
 
12. Language English=en en
 
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