Global testing under the sparse alternatives for single index models

Qian Lin, Zhigen Zhao, Jun S. Liu

For the single index model $y=f({\beta }^{\tau }x,\epsilon )$ with Gaussian design, %satisfying that rank $var(\mathbb{E}[x\mid y])=1$ where $f$ is unknown and $\beta$ is a sparse $p$-dimensional unit vect…