Testing and estimation in orthosymmetric Gaussian sequence model

Zeyu Jia, Yury Polyanskiy

We study the Gaussian sequence model, i.e. $X\sim N(\hat{\mathbf{I}}¸,I_{\infty })$, where $\hat{\mathbf{I}}¸\in \hat{I}“\subset {\ell }_2$ is assumed to be convex and compact. We show that goodness-of-fit…