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

   
@article{EJP137,
	author = {Zhi-Dong Bai and Hsien-Kuei Hwang and Tsung-Hsi Tsai},
	title = {Berry-Esseen Bounds for the Number of Maxima in Planar Regions},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {8},
	year = {2003},
	keywords = {Dominance, Maximal points, Central limit theorem, Berry-Esseen bound, Local limit theorem, Method of moments},
	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.},
	pages = {no. 9, 1-26},
	issn = {1083-6489},
	doi = {10.1214/EJP.v8-137},    
        url = {http://ejp.ejpecp.org/article/view/137}}