A Fourier Analytical Approach to Estimation of Smooth Functions in Gaussian Shift Model

Fan Zhou, Ping Li

Let ${\mathbf{x}}_j=\theta +{\epsilon }_j$, $j=1,\dots ,n$ be i.i.d. copies of a Gaussian random vector $\mathbf{x}\sim \mathcal{N}(\theta ,\mathbf{\Sigma })$ with unknown mean $\mathbfθ \i…