BEGIN:VCALENDAR
PRODID:-//eluceo/ical//2.0/EN
VERSION:2.0
CALSCALE:GREGORIAN
BEGIN:VEVENT
UID:www.tcs.tifr.res.in/event/766
DTSTAMP:20230914T125937Z
SUMMARY:Large Sample Behaviour of High Dimensional Autocovariance Matrices
with Application
DESCRIPTION:Speaker: Arup Bose (Indian Statistical Institute\nStatistics an
d Mathematics Unit\n203\, Barrackpore Trunk Road\nKolkata 700108)\n\nAbstr
act: \nConsider a sample of size $n$ from a linear process of dimension $p
$ where $n\, p \\to \\infty$\, $p/n \\to y \\in [0\, \\ \\infty).$ Let $
\\hat{\\Gamma}_{u}$ be the sample autocovariance of order $u$.\n\nThe exis
tence of limiting spectral distribution (LSD) of $\\hat{\\Gamma}_{u} + \\h
at{\\Gamma}_{u}^{*}$\, the symmetric sum of the sample autocovariance matr
ix $\\hat{\\Gamma}_{u}$ of order $u$\, is known in the literature under
appropriate (strong) assumptions on the coefficient matrices. Under signif
icantly weaker conditions\, we prove\, in a unified way\, that the LSD of
any symmetric polynomial in these matrices such as $\\hat{\\Gamma}_{u} +
\\hat{\\Gamma}_{u}^{*}$\, $\\hat{\\Gamma}_{u}\\hat{\\Gamma}_{u}^{*}$\,
$\\hat{\\Gamma}_{u} \\hat{\\Gamma}_{u}^{*}$+$\\hat{\\Gamma}_{k}\\hat{\\Ga
mma}_{k}^{*}$ exist. \n\nOur approach is through the more intuitive algeb
raic method of free probability that is applicable after an appropriate em
bedding\, in conjunction with the method of moments. Thus\, we are able to
provide a general description for the limits in terms of some freely inde
pendent variables.\n\nAll the previous results follow as special cases.\n\
nWe suggest statistical uses of these LSD and related results in problems
such as order determination and white noise testing.\n
URL:https://www.tcs.tifr.res.in/web/events/766
DTSTART;TZID=Asia/Kolkata:20170331T150000
DTEND;TZID=Asia/Kolkata:20170331T160000
LOCATION:AG-66 (Lecture Theatre)
END:VEVENT
END:VCALENDAR