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UID:7752@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160919T140000
DTEND;TZID=Europe/Paris:20160919T150000
DTSTAMP:20241120T204821Z
URL:https://www.i2m.univ-amu.fr/evenements/errors-in-variables-models-in-l
 arge-noise-regime/
SUMMARY: (...): Errors in variables models in large noise regime
DESCRIPTION::  The talk deals with estimating unknown parameters $a\,b\\in\
 \mathbb{R}$ in the simple Errors-in-Variables (EiV) linear model $Y_i=a+bX
 _i+\\epsilon_n\\xi_i$\; $ Z_i=X_i+\\sigma_n\\zeta_i$\, where $i=1\,\\ldots
 \,n$\, $\\xi_i\,\\\, \\zeta_i$ are i.i.d. standard Gaussian random variabl
 es\, $X_i\\in\\mathbb{R}$ are unknown nuisance variables\, and $\\epsilon_
 n\,\\sigma_n$ are noise levels which are assumed to be known.It is well kn
 own that the standard maximum likelihood estimates of $a\,\\\, b$ haven't 
 bounded moments. In order to improve these estimates\, we study the EiV mo
 del in the so-called Large Noise Regime assuming that $n\\rightarrow \\inf
 ty$\, but $\\epsilon_n^2=\\sqrt{n}\\epsilon_\\circ^2$\, $\\sigma_n^2=\\sqr
 t{n}\\sigma_\\circ^2$ with $\\epsilon_\\circ^2\,\\sigma_\\circ^2>0$. Under
  these assumptions\, the minimax approach to estimating $a\,b$ is develope
 d. In particular\, it is shown that the minimax estimate of $b$ is a solut
 ion to a convex optimization problem and a fast algorithm for computing th
 is estimate is proposed.
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TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
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DTSTART:20160327T030000
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