摘要：Suppose that we observe $y\in\mathbb{R}^{n}$ and $X\in\mathbb{R}^{n\times m}$ in the following errors-in-variables model: \begin{eqnarray*}y&=&X_{0}\beta^{*}+\epsilon\\X&=&X_{0}+W\end{eqnarray*} where $X_{0}$ is an $n\times m$ design matrix with independent subgaussian row vectors, $\epsilon\in\mathbb{R}^{n}$ is a noise vector and $W$ is a mean zero $n\times m$ random noise matrix with independent subgaussian column vectors, independent of $X_{0}$ and $\epsilon$. This model is significantly different from those analyzed in the literature in the sense that we allow the measurement error for each covariate to be a dependent vector across its $n$ observations. Such error structures appear in the science literature when modeling the trial-to-trial fluctuations in response strength shared across a set of neurons.
