NDLI: A Coincidence-Based Test for Uniformity Given Very Sparsely Sampled Discrete Data

Content Provider	IEEE Xplore Digital Library
Author	Paninski, L.
Copyright Year	1963
Abstract	How many independent samples N do we need from a distribution p to decide that p is epsiv-distant from uniform in an L₁ sense, Sigma_i=1 ^m \|p(i) - 1/m\| > epsiv? (Here m is the number of bins on which the distribution is supported, and is assumed known a priori.) Somewhat surprisingly, we only need N epsiv² Gt m ^1/2 to make this decision reliably (this condition is both sufficient and necessary). The test for uniformity introduced here is based on the number of observed ldquocoincidencesrdquo (samples that fall into the same bin), the mean and variance of which may be computed explicitly for the uniform distribution and bounded nonparametrically for any distribution that is known to be epsiv-distant from uniform. Some connections to the classical birthday problem are noted.
Sponsorship	IEEE Information Theory Society
Starting Page	4750
Ending Page	4755
Page Count	6
File Size	306587
File Format	PDF
ISSN	00189448
Volume Number	54
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Testing Entropy Statistical distributions Distributed computing Minimax techniques Engineering profession Computer errors Computer science Statistical analysis Upper bound minimax Convex bounds hypothesis testing
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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