High-dimensional semi-supervised learning: in search for optimal inference of the mean

We provide a high-dimensional semi-supervised inference framework focused on mean and variance of the response. Our data are comprised of an extensive of observations regarding the covariate vectors and a much smaller set of observations where we observe both the response as well as the. We allow the size of the covariates to be much larger than the size and impose weak conditions on a statistical form of the data. We new estimators of the mean and variance of the response that extend of the recent results presented in low-dimensional models. In particular, times we will not necessitate consistent estimation of the functional form the data. Together with estimation of the population mean and variance, we their asymptotic distribution and confidence intervals where we gains in efficiency compared to the sample mean and variance. Our, with minor modifications, is then presented to make important regarding inference about average treatment effects. We also the robustness of estimation and coverage and showcase widespread and generality of the proposed method.