Smoothing of Samples for Maxima

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Simple, efficient maxima-finding algorithms for multidimensional samples

New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The expected complexity of some measures related to the performance of the algorithms is analyzed. We also compare the efficiency of the algorithms with a few major...

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Maxima-finding algorithms for multidimensional samples: A two-phase approach

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

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.

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ژورنال

عنوان ژورنال: The Annals of Statistics

سال: 1981

ISSN: 0090-5364

DOI: 10.1214/aos/1176345333