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X-WR-CALNAME:Department of Statistics and Operations Research
X-ORIGINAL-URL:http://stat-or.unc.edu
X-WR-CALDESC:Events for Department of Statistics and Operations Research
BEGIN:VEVENT
DTSTART;TZID=UTC-4:20170306T153000
DTEND;TZID=UTC-4:20170306T163000
DTSTAMP:20171121T004857
CREATED:20170117T150343Z
LAST-MODIFIED:20170221T162152Z
UID:2582-1488814200-1488817800@stat-or.unc.edu
SUMMARY:STOR Colloquium: Zhiyi Zhang\, UNC Charlotte
DESCRIPTION:Zhiyi Zhang \nUniversity of North Carolina at Charlotte \nTitle: Statistical Implications of Turing’s Formula \n \nAbstract: This talk is organized into three parts. \n \n\nTuring’s formula is introduced. Given an iid sample from a countable alphabet under a probability distribution\, Turing’s formula (introduced by Good (1953)\, hence also known as the Good-Turing formula) is a mind-bending non-parametric estimator of total probability associated with letters of the alphabet that are NOT represented in the sample. Many of its statistical properties were not clearly known for a stretch of nearly sixty years until recently. Some of the newly established results\, including various asymptotic normal laws\, are described.\n\n \n\nTuring’s perspective is described. Turing’s formula brought about a new perspective (or a new characterization) of probability distributions on general countable alphabets. The new perspective in turn provides a new way to do statistics on alphabets\, where the usual statistical concepts associated with random variables (on the real line) no longer exist\, for example\, moments\, tails\, coefficients of correlation\, characteristic functions don’t exist on alphabets (a major challenge of modern data sciences). The new perspective\, in the form of entropic basis\, is introduced.\n\n \n\nSeveral applications are presented\, including estimation of information entropy and diversity indices.\n\n
URL:http://stat-or.unc.edu/event/stor-colloquium-zhiyi-zhang-unc-charlotte
CATEGORIES:STOR Colloquium
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