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We provide finite sample bounds on the Normal approximation to the law of theleast squares estimator of the projection parameters normalized by thesandwich-based standard errors. Our results hold in the increasing dimensionsetting and under minimal assumptions on the data generating distribution. Inparticular, we do not assume a linear regression function and only require theexistence of finitely many moments for the response and the covariates.Furthermore, we construct confidence sets for the projection parameters in theform of hyper-rectangles and establish finite sample bounds on their coverageand accuracy. We derive analogous results for partial correlations among theentries of sub-Gaussian vectors. \end{abstract}

Berry-Esseen Bounds for Projection Parameters and Partial Correlations with Increasing Dimension