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Berry-Esseen Bounds for the Number of Maxima in Planar Regions


 
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1. Title Title of document Berry-Esseen Bounds for the Number of Maxima in Planar Regions
 
2. Creator Author's name, affiliation, country Zhi-Dong Bai; National University of Singapore and Northeast Normal University
 
2. Creator Author's name, affiliation, country Hsien-Kuei Hwang; Academia Sinica, Taipei
 
2. Creator Author's name, affiliation, country Tsung-Hsi Tsai; Academia Sinica, Taipei
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Dominance, Maximal points, Central limit theorem, Berry-Esseen bound, Local limit theorem, Method of moments
 
4. Description Abstract We derive the optimal convergence rate $O(n^{-1/4})$ in the central limit theorem for the number of maxima in random samples chosen uniformly at random from the right equilateral triangle with two sides parallel to the axes, the hypotenuse with the slope $-1$ and consituting the top part of the boundary of the triangle. A local limit theorem with rate is also derived. The result is then applied to the number of maxima in general planar regions (upper-bounded by some smooth decreasing curves) for which a near-optimal convergence rate to the normal distribution is established.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2003-06-10
 
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/137
 
10. Identifier Digital Object Identifier 10.1214/EJP.v8-137
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 8
 
12. Language English=en
 
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