Minimax and adaptive estimation of general linear functionals under sparsity

Jie Xie, Dongming Huang

We study nonasymptotic minimax estimation of the linear functional $L(\hat{I}¸)=\hat{I}{\cdot }^{\top }\hat{I}¸$ for a high-dimensional $s$-sparse mean vector with an arbitrary loading vector $\hat{I}\cdot$. For symme…