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Graphical structures for geometric d...

Arias-Castro, Ery.

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Graphical structures for geometric detection.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Graphical structures for geometric detection./
Author:	Arias-Castro, Ery.
Description:	94 p.
Notes:	Source: Dissertation Abstracts International, Volume: 65-09, Section: B, page: 4645.
Contained By:	Dissertation Abstracts International65-09B.
Subject:	Statistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3145457
ISBN:	0496043609

Graphical structures for geometric detection.
Arias-Castro, Ery.

Graphical structures for geometric detection. - 94 p.

Source: Dissertation Abstracts International, Volume: 65-09, Section: B, page: 4645.

Thesis (Ph.D.)--Stanford University, 2004.

We observe n points in the unit d-dimensional hypercube. We want to know whether these points are uniformly distributed or whether a small fraction of them are actually concentrated near an object, such as a curve or sheet, which is only known to belong to some regularity class.

ISBN: 0496043609Subjects--Topical Terms:

517247
Statistics.

Graphical structures for geometric detection.
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100 1 $a Arias-Castro, Ery. $3 1932826
245 1 0 $a Graphical structures for geometric detection.
300 $a 94 p.
500 $a Source: Dissertation Abstracts International, Volume: 65-09, Section: B, page: 4645.
500 $a Adviser: David L. Donoho.
502 $a Thesis (Ph.D.)--Stanford University, 2004.
520 $a We observe n points in the unit d-dimensional hypercube. We want to know whether these points are uniformly distributed or whether a small fraction of them are actually concentrated near an object, such as a curve or sheet, which is only known to belong to some regularity class.
520 $a We argue that this hypothesis testing problem is relevant for the task of detecting structures in galaxy distributions.
520 $a We consider classes of Holder immersions and study the asymptotic power of the Generalized Likelihood Ratio Test (GLRT), or Scan Statistic, in this setting.
520 $a To each regularity class we associate a graphical structure designed to approximate the GLRT. Computing such approximations is challenging and some approaches are surveyed in the Computer Science and Operations Research literatures.
520 $a The detection performance of the Longest Significant Run Test is also investigated.
520 $a We extend this study to higher order contact, which models recent experiments in Perceptual Psychophysics; and to detection in graphs, which models networks of sensors.
590 $a School code: 0212.
650 4 $a Statistics. $3 517247
690 $a 0463
710 2 0 $a Stanford University. $3 754827
773 0 $t Dissertation Abstracts International $g 65-09B.
790 1 0 $a Donoho, David L., $e advisor
790 $a 0212
791 $a Ph.D.
792 $a 2004
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3145457