BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Sharp Constants in Normal an Edgeworth Approximation
DTSTART;VALUE=DATE-TIME:20220804T070000Z
DTEND;VALUE=DATE-TIME:20220804T072000Z
DTSTAMP;VALUE=DATE-TIME:20231210T055332Z
UID:indico-contribution-1211@conference2.aau.at
DESCRIPTION:We all know and love the central limit theorem (CLT) but there
is a lot more to wish for. The Berry-Esseen theorem overestimates the act
ual error in the CLT and truly sharp error bounds for specific distributio
ns are\, as far as we are aware\, only known in binomial cases and can be
found in Schulz (2016). Even less seems to be known for other distances an
d higher-order approximations.\n\nIn order to make progress here we consid
er it to be advisable to solve these problems for specific distributions s
uch as the binomial and the uniform distribution first. These are interest
ing in their own right and hopefully our solutions via Fourier inversion c
an be generalized to a wider set of distributions.\n\nTo give an example w
e plan to present the following two results. We found that the optimal bou
nd in the local CLT for the symmetric binomial distribution is \n\\begin{g
ather}\n \\frac{1}{2\\sqrt{2\\pi} n^{3/2}}\n\\end{gather}\nand in the g
lobal CLT with simple continuity correction it is \n\n\\begin{gather}\n 2
\\Phi\\bigg(-\\frac{3}{\\sqrt{2}}\\bigg) \\frac{1}{n}\n\\end{gather}\n\nwh
ere $\\Phi$ is the standard normal distribution function.\n\n$\\textbf{Ref
erences}$\nSchulz\, J. (2016). The Optimal Berry-Esseen Constant in the Bi
nomial Case. Dissertation\, Universität Trier. http://ubt.opus.hbz-nrw.de
/volltexte/2016/1007/.\n\nhttps://conference2.aau.at/event/131/contributio
ns/1211/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1211/
END:VEVENT
END:VCALENDAR