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

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