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DTSTART:20241027T030000
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UID:calendar.7998.field_data_news.0@dse.unibg.it
DTSTAMP:20241010T112348Z
CREATED:20240920T155737Z
DESCRIPTION:2024-10-02 12:30 - 13:30\n\n\nStatistics Seminar Series - Cecil
e Durot (Université Paris Nanterre)\n\n\n\nTitle: Minimax Optimal rates of
convergence in the shuffled regression\, unlinked regression\, and deconv
olution under vanishing noise\n\n \n\nCo-author: Debarghya Mukherjee\n\n
\n\nAbstract:Shuffled regression and unlinked regression represent intrigu
ing challenges that have garnered considerable attention in many fields\,
including but not limited to ecological regression\, multi-target tracking
problems\, image denoising\, etc. However\, a notable gap exists in the e
xisting literature\, particularly in vanishing noise\, i.e.\, how the rate
of estimation of the underlying signal scales with the error variance. Th
is paper aims to bridge this gap by delving into the monotone function est
imation problem under vanishing noise variance\, i.e.\, we allow the error
variance to go to $0$ as the number of observations increases. Our invest
igation reveals that\, asymptotically\, the shuffled regression problem ex
hibits a comparatively simpler nature than the unlinked regression\; if th
e error variance is smaller than a threshold\, then the minimax risk of th
e shuffled regression is smaller than that of the unlinked regression. On
the other hand\, the minimax estimation error is of the same order in the
two problems if the noise level is larger than that threshold. Our analysi
s is quite general in that we do not assume any smoothness of the underlyi
ng monotone link function. Because these problems are related to deconvolu
tion\, we also provide bounds for deconvolution in a similar context. Thro
ugh this exploration\, we contribute to understanding the intricate relati
onships between these statistical problems and shed light on their behavio
rs when subjected to the nuanced constraint of vanishing noise.\n\n \n\nLi
nk Google Meet:https://meet.google.com/hbm-aqhu-ank
DTSTART;TZID=Europe/Rome:20241002T123000
DTEND;TZID=Europe/Rome:20241002T133000
LAST-MODIFIED:20240920T161004Z
LOCATION:Aula 22 (Caniana) e Google Meet
SUMMARY:Statistics Seminar Series - Cecile Durot (Université Paris Nanterre
)
URL;TYPE=URI:https://dse.unibg.it/it/eventi/statistics-seminar-series-cecil
e-durot-universite-paris-nanterre
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