The focused information criterion for model selection is constructed to select the model that best estimates a particular quantity of interest, the focus, in terms of mean squared error. We extend this focused selection process to the high-dimensional regression setting with potentially a larger...

We study partially linear single-index models where both model parts may contain highdimensional variables. While the single-index part is of fixed dimension, the dimension of the linear part is allowed to grow with the sample size. Due to the addition of penalty terms to the loss function in...