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SUMMARY:Law of Large Numbers and Central Limit Theorem under Uncertainty o
f Probability Distributions
DTSTART;VALUE=DATE-TIME:20180829T120000Z
DTEND;VALUE=DATE-TIME:20180829T124000Z
DTSTAMP;VALUE=DATE-TIME:20210622T080636Z
UID:indico-contribution-3195@indico.math.cnrs.fr
DESCRIPTION:Speakers: Shige Peng (Shandong University)\nHow to calculate t
he essential uncertainty of probability distributions hidden behind a real
data sequence is a theoretically and practically important challenging
problem.\n\nRecently some fundamentally important progresses have been ach
ieved in the domain of law of large numbers (LLN) and central limit theor
em (CLT) with a much weaker assumption of independence and identical distr
ibution (i.i.d.) under a sublinear expectation. \n\nThese new LLN and CTL
can be applied to a significantly wide classes of data sequence to constr
uct the corresponding optimal estimators. In particular\, many distributio
n uncertainties hidden behind data sequences are able to be quantitativel
y calculated by introducing a new algorithm of phi-max-mean type. \n\nI
n this talk\, I take some typical examples to provide a more concrete expl
anation of the above mentioned LLN and CLT\, the key idea of their proofs\
, as well as the new phi-max-mean estimators.\n\nhttps://indico.math.cnrs
.fr/event/3123/contributions/3195/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3195/
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