Yuri Golubev – Errors in variables models in large noise regime

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Date(s) - 19 septembre 2016

Catégories Pas de Catégories

The talk deals with estimating unknown parameters $a,b\in\mathbbR$ 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 variables, $X_i\in\mathbbR$ are unknown nuisance variables, and $\epsilon_n,\sigma_n$ are noise levels which are assumed to be known.It is well known that the standard maximum likelihood estimates of $a,, b$ haven’t bounded moments. In order to improve these estimates, we study the EiV model in the so-called Large Noise Regime assuming that $n\rightarrow \infty$, but $\epsilon_n^2=\sqrtn\epsilon_\circ^2$, $\sigma_n^2=\sqrtn\sigma_\circ^2$ with $\epsilon_\circ^2,\sigma_\circ^2>0$. Under these assumptions, the minimax approach to estimating $a,b$ is developed. In particular, it is shown that the minimax estimate of $b$ is a solution to a convex optimization problem and a fast algorithm for computing this estimate is proposed.[