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We consider the problem of estimating an unknown parameter vector ${\boldsymbol \theta}\in{\mathbb R}^n$, given noisy observations ${\boldsymbol Y} = {\boldsymbol \theta}{\boldsymbol \theta}^{\top}/\sqrt{n}+{\boldsymbol Z}$ of the rank-one matrix ${\boldsymbol \theta}{\boldsymbol \theta}^{\top}$, where ${\boldsymbol Z}$ has independent Gaussian entries.
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