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In this paper, we present a new and effective simulation-based approach toconduct both finite- and large-sample inference for high-dimensional linearregression models. This approach is developed under the so-called repro samplesframework, in which we conduct statistical inference by creating and studyingthe behavior of artificial samples that are obtained by mimicking the samplingmechanism of the data. We obtain confidence sets for (a) the true modelcorresponding to the nonzero coefficients, (b) a single or any collection ofregression coefficients, and (c) both the model and regression coefficientsjointly. We also extend our approaches to drawing inferences on functions ofthe regression coefficients. The proposed approach fills in two major gaps inthe high-dimensional regression literature: (1) lack of effective approaches toaddress model selection uncertainty and provide valid inference for theunderlying true model; (2) lack of effective inference approaches thatguarantee finite-sample performances. We provide both finite-sample andasymptotic results to theoretically guarantee the performances of the proposedmethods. In addition, our numerical results demonstrate that the proposedmethods are valid and achieve better coverage with smaller confidence sets thanthe existing state-of-art approaches, such as debiasing and bootstrapapproaches.

Finite- and Large- Sample Inference for Model and Coefficients in High-dimensional Linear Regression with Repro Samples